Nonlinear Phenomena, Chaos, Control and Applications to Engineering and Science and Experimental Aspects of Complex Systems: 1st Edition

1. Summary

In this Topic, 34 (thirty-four) papers were selected and published on the following sub-themes: Modeling and Nonlinear Systems (Contributions 1–5); Control, Synchronization, and Optimization (Contributions 6–13); Chaos and Hyperchaos (Contributions 3 and 14–20); Complex Systems (Contributions 21–25); and Applications to Engineering and Sciences (Contributions 22 and 26–32).

The distribution of papers among MDPI journals is as follows: Symmetry (5 papers), Entropy (5 papers), Machines (3 papers), Dynamics (2 papers), Applied Sciences (11 papers), Mathematics (7 papers), and Axioms (1 paper).

The authors came from the following countries: China, Norway, Hong Kong, Japan, Romania, Turkey, Russia, Saudi Arabia, Italy, the United States, and Thailand.

This Editorial is organized as follows: the main contributions to this Topic are described in Section 2, and future work in development is presented in Section 3.

2. Contributed Papers

In this section, we will summarize the 34 (thirty-four) contributions to this Topic, considering the following: the formulation or evolution of overarching research goals and aims, the development or design of methodology, the creation of models, and the application of mathematical, computational, experimental, or other formal techniques to analyze or synthesize the study data.

In Contribution 1, Yuexin Wang et al. dealt with the ability of each oscillator in the coupled Stuart–Landau oscillator system, with Erdős–Rényi random graph network topology, to affect the dynamic survivability. Following this analysis, the maintenance of symmetry phenomenon synchronization was considered as the key mission to be completed. Inspired by the study of dynamic survivability, a new centrality index called dynamic survivability centrality was constructed, which is determined by the degree of the oscillator and the size of the system. The proposed index compensates for the limitation of traditional indices that solely consider network structure, thereby enabling a more accurate assessment of node influence on the normal operation of dynamic systems.

In Contribution 6, Zhifu Jia addressed dynamic game problems involving uncertainty, delays, and jumps using uncertain delay differential equations with jumps. A linear quadratic differential game was studied in this context, transforming the problem into a finite-dimensional form using the Z(x,y) transform. The existence of a Nash equilibrium was shown to depend on solutions to cross-coupled Riccati equations. A saddle point equilibrium strategy was also derived and applied to a carbon emission reduction game.

An industrial robot experiment was designed to test the vibration suppression method proposed by Liang Liang et al. in Contribution 7. It can reduce the maximum acceleration amplitude of residual vibration by 62% and the vibration duration by 71%. Compared with the input shaping method, the method proposed can also reduce the terminal residual vibration more effectively and ensure the consistency of running time and trajectory.

In Contribution 26, Yong Zhang et al. presented a study on rubbing-induced vibration characteristics considering the flexibility of coated casings and blades. The obtained results showed that the coating can diminish the severity level of rubbing and the material and thickness of the coating changed the nodal diameter vibrations of the casings (NDVCs) induced by rubbing. This study provided valuable guidance for the optimization and design of blade–casing systems.

A special vibration damper was proposed by Chun-Nam Wong et al. in Contribution 27 for Young’s modulus and hardness identification through a scratching process on extruded aluminum. The paper presented the design and working principle of the scratching damper based on a scratching device, and a non-contact electromagnetic shaker was used to generate the shaking force for the test sample vibration.

In Contribution 28, Parindra Kusriantoko et al. studied different CFD-codes for fluidized beds. The authors highlighted the significant influence of restitution coefficients on bed expansion due to their effect on particle–particle collisions, with a value of 0.9 deemed optimal for balancing simulation accuracy and computational efficiency. Conversely, the secularity coefficient, impacting particle–wall interactions, exhibited a more subtle effect on bed dynamics. This finding emphasized the critical role of carefully choosing these coefficients to effectively simulate the nuanced behaviors of fluidized beds.

In Contribution 21, Jiehui Liu et al. studied PMT fluorescence signal denoising processing. The focus was on the impact of noise interference on weak electrical signals and wavelet transform was used to denoise the signals. At the same time, considering that the photoelectric system was susceptible to temperature changes, a multiparameter fitting model was constructed, and a BP neural network was used to further process the signal, separating the real data from the original data. Finally, a high-precision and wide-range trace level sulfur dioxide concentration detection device and algorithm were obtained with success.

The attached flow method for solving reaction–diffusion processes described by a generalized Dodd–Bullough–Mikhailov equation was studied by Carmen Ionescu and Iulian Petrisor in Contribution 29. The method involves reducing the equation’s order and explicitly introducing the flow variable through decomposition. This approach avoids complex integral solutions and enables accurate analytical results. It is applied to the generalized Dodd–Bullough–Mikhailov equation with nonlinearities up to the fifth order, with solutions analyzed based on parameter values.

In Contribution 22, Akio Tsuneda presented an analysis of the auto-correlation functions of chaotic binary sequences generated from a one-dimensional chaotic map using two binary functions applied alternately. Two similar methods were described, deriving the theoretical auto-correlation functions of the resulting binary sequences, expressed in terms of the auto- and cross-correlation functions of the sequences generated by each binary function individually. Numerical experiments were also conducted to validate the theoretical results.

In Contribution 33, Houxiang Wang and Jiaqing Chen proposed an improved switching linear dynamical system model that captures complex dynamics using higher-order autoregressive processes and flexible state transitions via stick-breaking logistic regression. Efficient inference is enabled through Pólya-gamma augmentation. The model outperforms existing methods on synthetic and fMRI data.

A new chaos-based image encryption algorithm that combines discrete Fourier transform and Joseph traversal to encrypt images in both frequency and spatial domains was proposed by Mingxu Wang, Xianping Fu, Xiaopeng Yan, and Lin Teng in Contribution 23. It uses a logistic map for chaos generation, variable-step Joseph traversal for scrambling, and block diffusion. The method enhances security and shows strong resistance to common attacks.

In Contribution 14, Erman Ozpolat andArif Gulten, explored the synchronization and implementation of a novel hyperchaotic system using an adaptive observer. Hyperchaotic systems, known for possessing a greater number of positive Lyapunov exponents compared to chaotic systems, present unique challenges and opportunities in control and synchronization. In this study, the authors introduced a novel hyperchaotic system, thoroughly examining its dynamic properties and conducting a comprehensive phase space analysis. The proposed hyperchaotic system underwent validation through circuit simulation to confirm its behavior. By introducing an adaptive observer synchronization technique, the authors successfully synchronized the dynamics of the novel hyperchaotic system with an identical counterpart. Importantly, Contribution 14 extends the application of this synchronization method to the domain of secure communication, showcasing its practical usage.

In Contribution 34, Maxim Shishlenin, Andrey Kozelkov, and Nikita Novikov showed the fundamental possibility of constructing a computational digital twin of the acoustic tomograph within the framework of a unified physics–mathematical model, based on the Navier–Stokes equations. The authors suggested that the size of the modeling area is quite small, sound waves are waves of “small” disturbance, and given that a person consists of more than 60% water, human organs can be modeled using a liquid model, considering their density. The results showed that the developed technology can be used to probe the human body in medical acoustic tomographs and determine its acoustic parameters to detect neoplasms.

In Contribution 8, Zihao Lu, Na Wang, and Shigui Dong considered nonlinear discrete systems with dual unknown inputs and proposed two new improved squared-root cubature Kalman filtering (ISRCKF) algorithms to estimate system states and dual unknown inputs. Improved square-root cubature Kalman filtering 1 (ISRCKF1) introduces an innovation that first obtains the unknown input estimated from the measurement equation, then updates the innovation to derive the unknown input estimates from the state equation, and uses the already obtained estimates of the dual unknown inputs to corrected the one-step estimate of the state; finally, the minimum variance unbiased estimate of the state is obtained. For many years, chaotic maps have been widely used in the design of various algorithms in cryptographic systems.

In Contribution 15, Lijun Zhang, Caochuan Ma, Yuxiang Zhao, and Wenbo Zhao introduced a compound chaotic system using quantum random walks controlled by a hyperchaotic map and proposed a novel method for dynamically generating S-Boxes. The system exhibits high randomness and complexity. The generated S-Boxes meet key cryptographic criteria and demonstrate excellent performance, making the method suitable for secure information systems. In addition, the proposed dynamic S-Box construction technique can be used to generate cryptographically strong substitution-boxes in practical information security systems.

An investigation into the dynamic states and relative intensity noise of laser diodes subjected to double optical feedback was conducted by Salah Abdulrhmann, Abu Mohamed Alhasan, and A. Y. Madkhli in Contribution 30. They employed modified and improved time-delay rate equations to account for double external optical feedback. The dynamic states and noise of lasers were investigated using bifurcation diagrams of the output photon number, its temporal variations, and the intensity noise of the laser. This analysis considered feedback strengths due to the double external cavity and their spacing from the front facet of the laser with and without phase due to feedback. The results revealed that considering phase causes significant variations in laser intensity and a phase shift in the temporal variations in the laser output. This results in relative intensity noise suppression and a frequency shift in the intensity noise spectrum. These findings represented new contributions to our understanding of the reliance of lasing frequency shift on the phase due to feedback, regardless of whether feedback originates from a single or double external cavity.

Xiaonan Yao, Gang Zhang, Song Yang, and Yuehua Chen used the sliding-mode control-based adaptive anti-disturbance strategy with success in Contribution 9, and the simulation results demonstrated that the control strategy proposed in this paper shows resistance to system uncertainties and unknown external disturbances. Furthermore, it reduces the model accuracy requirements for the controller and proves to be suitable for accurately controlling dissolved oxygen in circulating water systems.

In Contribution 16, Li-Jun Ouyang, Bing-Qing Xie, and Bin Ding analytically explored approximate lag and anticipating synchronization between two unidirectionally coupled hyperchaotic Chen systems without time-delay coupling. By treating lag synchronization as a form of generalized synchronization, the authors derived conditions independent of time delay. Using Taylor expansions, they showed how to recreate past or predict future signals, offering a simple method to counteract the effects of signal transmission delays in hyperchaotic systems.

In Contribution 31, Ruoshi Yang et al. considered a mechanical model of an elastic bar embedded in an elastic and viscoelastic medium, fixed at the base and free at the top, which was established based on the Winkler foundation assumption. The deflection function of a bar subjected to both axial force and locally distributed horizontal load was derived using the Rayleigh–Ritz method. Utilizing the elastic–viscoelastic correspondence principle, the viscoelastic medium surrounding the bar was modeled as an elastic medium in which the ground reaction coefficient varies within phase space formulation. This study provides a robust theoretical foundation for soft soil foundation engineering projects and fills a significant gap in the literature by offering a comprehensive framework for understanding displacement in elastic bars within viscoelastic media. Drawing upon the derivation of the deformation function for elastic rods within a viscoelastic medium, the findings of this research hold significant applicability across a range of domains. These include, but are not limited to, the expansion of roadways in regions characterized by coastal soft soil, as well as the successful monitoring of deformation and lifespan in bridge pile foundations.

Xiaochun Zhang, Jianhan Hu, and Shuyang Chen presented a mechanical model for an elastic bar embedded in a viscoelastic medium, reflecting the behavior of structures in coastal soft soil regions of China in Contribution 32. Using the Rayleigh–Ritz method and the Winkler foundation assumption, they derived the bar’s deflection under axial and horizontal loads and applied the elastic–viscoelastic correspondence principle to model soil behavior, providing a solid theoretical foundation for infrastructure projects on soft soil, such as road expansion and bridge foundation monitoring.

In Contribution 10, Simone Fiori, Luca Ciaramicoli, and Giovanni Berluti proposed a novel control strategy for a DC-DC electrical converter realized as a switched circuit. The present endeavor was based on early work by Leonard and Krishnaprasad where a prototypical DC-DC converter was modeled as a state space dynamical system and controlled by an open-loop strategy based on Lie group theory. In the present work, the authors introduced a closed-loop control strategy based on maximum convergence rate, studied some features of the novel method, and illustrated its behavior by numerical simulations. A numerical comparison of the two methods complemented the paper and showed how the proposed feedback control method outperforms the static one in terms of convergence rate and resiliency against parameter mismatch.

In Contribution 2, Dan Gu, Yufeng Xie, Shulin Liu, Yuan Wei, and Jiayi Shen investigated subtle faults in high-speed motorized spindles. A dynamical model considering unbalanced mass and spindle inclination faults was developed. The natural frequencies and mode shapes were analyzed using the whole transfer matrix method (WTMM). The results showed that spindle deflection varies with fault type and speed, with maximum deflection occurring at the third natural frequency. This paper also showed that different faults produce distinct mode shapes even at the same speed, which is helpful information in fault identification and diagnosis.

In Contribution 3, Zun Li, Binqiang Xue, and Youyuan Chen dealt with the proposal of an event-triggered state estimation method for parameter-uncertain systems with a binary encoding transmission scheme. The stability analysis showed that the state estimation error of the proposed method was bound. Finally, the practical value of the method proposed in this paper was confirmed through numerical simulations.

Bin Zhen and Yu Zhang proposed a new approach to realize generalized function projective synchronization (GFPS) between two different chaotic systems with uncertain parameters in Contribution 17. The GFPS condition was derived by converting the differential equations describing the synchronization error systems into a series of Volterra integral equations.

The hourglass buoy was compared by Houssein Yassin to a spherical buoy to illustrate differences in their response to regular waves and energy extraction when using the same control laws in Contribution 4. A spherical buoy diameter of 7.5 m was required to obtain the same power output as a 5 m tall hourglass buoy. A power-force-amplitude (PFA) metric was introduced to compare energy extraction performance and power take-off requirements. The hourglass buoy’s PFA was 13% larger than the spherical buoy, implying that it could produce similar power but with less control effort.

A dynamic model of the working mechanism of a compound pendulum jaw crusher with clearance was established by the Lagrange multiplier method (LMD) based on the L-N contact force model and modified Coulomb friction force model in Contribution 18. The results obtained by Shenpeng Wang, Yan Cui, and Chune Wang showed that, under the premise of meeting the requirements of crusher production capacity, increasing the driving speed and reducing the clearance size can weaken the shock and chaos phenomenon during the operation of the mechanism, improve the dynamic performance, and enhance the operation stability, and the service life of foundation was prolonged with the stability of vibration force. Furthermore, the optimal combination of driving speed and clearance size was determined, which provides a theoretical basis for the optimization of the vibration force of the jaw crusher.

An investigation of the formation problem of an array of large-scale mobile sensor networks was carried out by Xueming Qian and Baotong Cui in Contribution 11. A new framework for the dynamic of mobile sensors as a continuum described by the parabolic system with boundary disturbance was proposed. The communication topology of agents is a chain graph and fixed. Leader feedback laws which were designed in a manner to the boundary control of large-scale mobile sensor networks allow the mobile sensors to achieve the formation steadily. By referring to the Lyapunov functional method and employing a boundary control approach, a new protocol was established to deal with a formation problem for the large-scale mobile sensor networks.

In Contribution 24, Hongrui Wang et al. proposed a distributed double-layer model predictive control algorithm based on dual decomposition for multivariate constrained systems to reduce the computational complexity of process control, giving the optimal solution formulation of the optimization problem consisting of this objective function and the constraints. The algorithm proposed in this paper achieved control goals while significantly reducing the computational complexity and has research significance for promoting the industrial implementation of double-layer model predictive control with success.

A three-dimensional (3D) autonomous chaotic system was analyzed by Meng Liu, Zhaoyan Wu, and Xinchu Fu in Contribution 19. In the system, each equation contains a quadratic cross product. Additionally, an equivalent electronic circuit for the proposed chaotic system was designed according to Kirchhoff’s Law, and a corresponding response electronic circuit was also designed for identifying the unknown parameters or monitoring the changes in the system parameters. Moreover, numerical simulations were presented and complemented the theoretical results.

In Contribution 20, Qian Wei, Peng Su, Lin Zhou, and Wentao Shiin proposed a feedback optimization strategy of residual compensation to correct the trajectory prediction values and improve prediction accuracy. For the initial value sensitivity problem of the PSO model identification algorithm, a new initial population strategy was proposed, which improved the effectiveness of initial parameters on model identification. Through simulation experiment analysis, it was verified that the proposed OTP-SSCT algorithm achieves better prediction accuracy and faster response time.

In Contribution 12, Dharma Raj Khatiwad dealt with the synchronization of an ensemble of oscillators, that is, a phenomenon that is present in systems of different fields, ranging from social to physical and biological systems. This phenomenon was often described mathematically by the Kuramoto model, which assumes oscillators of fixed natural frequencies connected by an equal and uniform coupling strength, with an analytical solution only possible for an infinite number of oscillators. However, most real-life synchronization systems consist of a finite number of oscillators and are often perturbed by external fields. The results obtained showed that the identical trends observed in the two cases give an important indication that the synchrony persists even under the influence of external factors, something very plausible in the context of real-life synchronization events. The occasional boosting of coupling strength is also enough to keep the assembly of oscillators in a synchronized state persistently.

In Contribution 5, Kornphong Chonsiripong et al. studied the N-species competitive coexistence model with direct effect on habitat destruction, to analyze the behaviors of abundant and extinct species in the system caused by habitat loss. In this paper, the proportional abundances of 50 species were numerically portrayed in each case. The authors found that the survival of a species is guaranteed if its corresponding eigenvalue is positive. However, the fact that a species has a negative corresponding eigenvalue does not guarantee its extinction, as this also depends on the initial number of that species.

The relationship between the Chinese market and the US market is of great interest for researchers and investors. In Contribution 25, Chun-Xiao Nie and Jing Xiao used transfer entropy and local random permutation (LRPLRP) surrogates to detect the information flow dynamics between the two markets. In this case, dynamic analysis based on weekly data showed that the information flow evolves and includes three significant periods between 2004 and 2021. They also used daily data to analyze the dynamics of information flow in detail over the three periods and found that changes in the intensity of information flow were accompanied by major events affecting the markets, such as the 2008 financial crisis and the COVID-19 pandemic period. In particular, the impact of the S&P500 index on different industry indices in the Chinese market was analyzed, and it was found that the dynamics of information flow exhibited multiple patterns. This study revealed the complex information flow between the two markets from the perspective of nonlinear dynamics, thereby helping to analyze the impact of major events and providing quantitative analysis tools for investment practice.

Finally, in Contribution 13, Pu Yang, Yu Ding, Ziwei Shen, and Kejia Feng studied the consensus fault-tolerant control problem of a class of second-order leader–follower multi-agent systems with unknown disturbance and actuator faults, and proposed an integral non-singular terminal sliding mode control algorithm based on a finite-time observer. First, a finite-time disturbance observer was designed based on a combination of high-order sliding mode and dual-layer adaptive rules to realize fast estimation and compensation of disturbance and faults. Then, a sliding surface with additional integral links was designed based on the conventional sliding surface, and an integral non-singular terminal sliding mode controller was proposed to realize the robust consensus in finite time and accurately diminish the chattering phenomena. Finally, a numerical example and simulation verified effectiveness.

The contributions are listed below:

• Wang, Y.; Sun, Z.; Ye, S.; Zhao, T.; Zhang, X.; Xu, W. Dynamic Survivability Centrality in Nonlinear Oscillator Systems. Symmetry 2024, 16, 1661. https://doi.org/10.3390/sym16121661.
• Gu, D.; Xie, Y.; Liu, S.; Wei, Y.; Shen, J. Dynamic Modeling of Motorized Spindle System with Unbalanced Mass and Spindle Inclination. Appl. Sci. 2023, 13, 10053. https://doi.org/10.3390/app131810053.
• Li, Z.; Xue, B.; Chen, Y. Event-Triggered State Estimation for Uncertain Systems with Binary Encoding Transmission Scheme. Mathematics 2023, 11, 3679. https://doi.org/10.3390/math11173679.
• Yassin, H.; Gonzalez, T.D.; Parker, G.; Wilson, D. Effect of the Dynamic Froude–Krylov Force on Energy Extraction from a Point Absorber Wave Energy Converter with an Hourglass-Shaped Buoy. Appl. Sci. 2023, 13, 4316. https://doi.org/10.3390/app13074316.
• Chonsiripong, K.; Duangdai, E.; Pongvuthithum, R.; Likasiri, C. Habitat Destruction and Restoration in Relation to Extinction and Survival of Species in Competitive Communities. Appl. Sci. 2022, 12, 8693. https://doi.org/10.3390/app12178693.
• Jia, Z. Equilibrium Control in Uncertain Linear Quadratic Differential Games with V-Jumps and State Delays: A Case Study on Carbon Emission Reduction. Entropy 2024, 26, 943. https://doi.org/10.3390/e26110943.
• Liang, L.; Wu, C.; Liu, S. A Terminal Residual Vibration Suppression Method of a Robot Based on Joint Trajectory Optimization. Machines 2024, 12, 537. https://doi.org/10.3390/machines12080537.
• Lu, Z.; Wang, N.; Dong, S. Improved Square-Root Cubature Kalman Filtering Algorithm for Nonlinear Systems with Dual Unknown Inputs. Mathematics 2024, 12, 99. https://doi.org/10.3390/math12010099.
• Yao, X.; Zhang, G.; Yang, S.; Chen, Y. Adaptive Anti-Disturbance Control of Dissolved Oxygen in Circulating Water Culture Systems. Symmetry 2023, 15, 2015. https://doi.org/10.3390/sym15112015.
• Fiori, S.; Ciaramicoli, L.; Berluti, G. Maximum Convergence Rate Control of a Switched Electrical Network with Symmetries. Symmetry 2023, 15, 1861. https://doi.org/10.3390/sym15101861.
• Qian, X.; Cui, B. A PDE Model Approach to Formation Control of Large-Scale Mobile Sensor Networks with Boundary Uncertainties. Axioms 2023, 12, 9. https://doi.org/10.3390/axioms12010009.
• Khatiwad, D.R. Numerical Solution of Finite Kuramoto Model with Time-Dependent Coupling Strength: Addressing Synchronization Events of Nature. Mathematics 2022, 10, 3633. https://doi.org/10.3390/math10193633.
• Yang, P.; Ding, Y.; Shen, Z.; Feng, K. Integral Non-Singular Terminal Sliding Mode Consensus Control for Multi-Agent Systems with Disturbance and Actuator Faults Based on Finite-Time Observer. Entropy 2022, 24, 1068. https://doi.org/10.3390/e24081068.
• Ozpolat, E.; Gulten, A. Synchronization and Application of a Novel Hyperchaotic System Based on Adaptive Observers. Appl. Sci. 2024, 14, 1311. https://doi.org/10.3390/app14031311.
• Zhang, L.; Ma, C.; Zhao, Y.; Zhao, W. A Novel Dynamic S-Box Generation Scheme Based on Quantum Random Walks Controlled by a Hyper-Chaotic Map. Mathematics 2024, 12, 84. https://doi.org/10.3390/math12010084.
• Ouyang, L.-J.; Xie, B.-Q.; Ding, B. Analytical Studies on Approximate Lag and Anticipating Synchronization in Two Unidirectionally Coupled Hyperchaotic Chen Systems without Time Delay. Appl. Sci. 2023, 13, 11949. https://doi.org/10.3390/app132111949.
• Zhen, B.; Zhang, Y. Generalized Function Projective Synchronization of Two Different Chaotic Systems with Uncertain Parameters. Appl. Sci. 2023, 13, 8135. https://doi.org/10.3390/app13148135.
• Wang, S.; Cui, Y.; Wang, C. Dynamics Analysis and Chaos Identification of Compound Pendulum Jaw Crusher with Joint Clearance. Appl. Sci. 2023, 13, 238. https://doi.org/10.3390/app13010238.
• Liu, M.; Wu, Z.; Fu, X. Dynamical Analysis of a One- and Two-Scroll Chaotic System. Mathematics 2022, 10, 4682. https://doi.org/10.3390/math10244682.
• Wei, Q.; Su, P.; Zhou, L.; Shi, W. Online Tracking of Maneuvering Target Trajectory Based on Chaotic Time Series Prediction. Entropy 2022, 24, 1668. https://doi.org/10.3390/e24111668.
• Liu, J.; Zhang, Y.; Li, J.; Zhao, Y.; Guo, J.; Yang, L.; Zhao, H. PMT fluorescence signal denoising processing based on wavelet transform and BP neural network. Appl. Sci. 2024, 14, 4866. https://doi.org/10.3390/app14114866.
• Tsuneda, A. Auto-Correlation Functions of Chaotic Binary Sequences Obtained by Alternating Two Binary Functions Bayesian Inference of Recurrent Switching Linear Dynamical Systems with Higher-Order Dependence. Dynamics 2024, 4, 272–286. https://doi.org/10.3390/dynamics4020016.
• Wang, M.; Fu, X.; Teng, X.Y.A. A new chaos-based image encryption algorithm based on discrete fourier transform and improved Joseph traversal. Mathematics 2024, 12, 638. https://doi.org/10.3390/math12050638.
• Wang, H.; Zhang, P.; Yang, Z.; Zou, T. Decomposition–Coordination of Double-Layer MPC for Constrained Systems. Entropy 2023, 25, 17. https://doi.org/10.3390/e25010017.
• Nie, C.-X.; Xiao, J. Dynamics of Information Flow between the Chinese A-Share Market and the U.S. Stock Market: From the 2008 Crisis to the COVID-19 Pandemic Period. Entropy 2022, 24, 1102. https://doi.org/10.3390/e24081102.
• Zhang, Y.; Yang, S.; Tai, X.; Ma, H.; Guan, H.; Mu, Q.; Qu, L.; Ding, X. Study on Rubbing-Induced Vibration Characteristics Considering the Flexibility of Coated Casings and Blades. Machines 2024, 12, 481. https://doi.org/10.3390/machines12070481.
• Wong, C.-N.; Vyas, A.; Wong, W.-O.; Sun, R. Young’s Modulus and Hardness Identification of Extruded Aluminum by Scratching Damper. Machines 2024, 12, 413. https://doi.org/10.3390/machines12060413.
• Kusriantoko, P.; Daun, P.F.; Einarsrud, K.E. A Comparative Study of Different CFD-codes for Fluidized Beds. Dynamics 2024, 4, 475–498. https://doi.org/10.3390/dynamics4020025.
• Ionescu, C.; Petrisor, I. Attached Flows for Reaction—Diffusion Processes Described by a Generalized Dodd—Bullough—Mikhailov Equation. Symmetry 2024, 16, 531. https://doi.org/10.3390/sym16050531.
• Abdulrhmann, S.; Alhasan, A.M.; Madkhli, A.Y. Dynamics of Semiconductor Laser Coupled with Two External Cavities. Appl. Sci. 2023, 13, 12827. https://doi.org/10.3390/app132312827.
• Yang, R.; Sun, W.; Le, M.; Zhang, H. The Chinese Aviation Network: An Empirical Temporal Analysis on Its Structural Properties and Robustness. Appl. Sci. 2023, 13, 11627. https://doi.org/10.3390/app132111627.
• Zhang, X.; Hu, J.; Chen, S. Study on Stability of Elastic Compression Bending Bar in Viscoelastic Medium. Appl. Sci. 2023, 13, 11111. https://doi.org/10.3390/app131911111.
• Wang, H.; Chen, J. Bayesian Inference of Recurrent Switching Linear Dynamical Systems with Higher-Order Dependence. Symmetry 2024, 16, 474. https://doi.org/10.3390/sym16040474.
• Shishlenin, M.; Kozelkov, A.; Novikov, N. Nonlinear Medical Ultrasound Tomography: 3D Modeling of Sound Wave Propagation in Human Tissues. Mathematics 2024, 12, 212. https://doi.org/10.3390/math12020212.

3. Future Work in Development

A second edition of the Topic “Nonlinear Phenomena, Chaos, Control and Applications to Engineering and Science and Experimental Aspects of Complex Systems” is in development. The collection will also provide a great opportunity for disseminating recent advances in analytical and numerical techniques, discussing novel phenomena and behaviors regarding several aspects of nonlinear dynamics and control, as was the case with the first edition.