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17 pages, 1210 KiB

Open AccessArticle

Nonlinear Dynamics of a General Stochastic SIR Model with Behavioral and Physical Changes: Analysis and Application to Zoonotic Tuberculosis

by Yassine Sabbar, Mohammad Izadi, Aeshah A. Raezah and Waleed Adel

Mathematics 2024, 12(13), 1974; https://doi.org/10.3390/math12131974 - 26 Jun 2024

Viewed by 1247

Abstract

This paper presents a comprehensive nonlinear analysis of an innovative stochastic epidemic model that accounts for both behavioral changes and physical discontinuities. Our research begins with the formulation of a perturbed model, integrating two general incidence functions and incorporating a Lévy measure to [...] Read more.

This paper presents a comprehensive nonlinear analysis of an innovative stochastic epidemic model that accounts for both behavioral changes and physical discontinuities. Our research begins with the formulation of a perturbed model, integrating two general incidence functions and incorporating a Lévy measure to account for independent jump components. We start by confirming the well-posed nature of the model, ensuring its mathematical soundness and feasibility for further analysis. Following this, we establish a global threshold criterion that serves to distinguish between the eradication and the persistence of an epidemic. This threshold is crucial for understanding the long-term behavior of a disease within a population. To rigorously validate the accuracy of this threshold, we conducted extensive numerical simulations using estimated data on Zoonotic Tuberculosis in Morocco. These simulations provide practical insights and reinforce the theoretical findings of our study. A notable aspect of our approach is its significant advancement over previous works in the literature. Our model not only offers a more comprehensive framework but also identifies optimal conditions under which an epidemic can be controlled or eradicated. Full article

(This article belongs to the Special Issue Dynamical System and Stochastic Analysis)

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15 pages, 295 KiB

Open AccessArticle

Existence and Hyers–Ulam Stability of Stochastic Delay Systems Governed by the Rosenblatt Process

by Ghada AlNemer, Mohamed Hosny, Ramalingam Udhayakumar and Ahmed M. Elshenhab

Mathematics 2024, 12(11), 1729; https://doi.org/10.3390/math12111729 - 2 Jun 2024

Viewed by 693

Abstract

Under the effect of the Rosenblatt process, time-delay systems of nonlinear stochastic delay differential equations are considered. Utilizing the delayed matrix functions and exact solutions for these systems, the existence and Hyers–Ulam stability results are derived. First, depending on the fixed point theory, [...] Read more.

Under the effect of the Rosenblatt process, time-delay systems of nonlinear stochastic delay differential equations are considered. Utilizing the delayed matrix functions and exact solutions for these systems, the existence and Hyers–Ulam stability results are derived. First, depending on the fixed point theory, the existence and uniqueness of solutions are proven. Next, sufficient criteria for the Hyers–Ulam stability are established. Ultimately, to illustrate the importance of the results, an example is provided. Full article

(This article belongs to the Special Issue Dynamical System and Stochastic Analysis)

14 pages, 372 KiB

Open AccessArticle

Distributed Interval Observers with Switching Topology Design for Cyber-Physical Systems

by Junchao Zhang, Jun Huang and Changjie Li

Mathematics 2024, 12(1), 163; https://doi.org/10.3390/math12010163 - 4 Jan 2024

Cited by 1 | Viewed by 956

Abstract

In this paper, the distributed interval estimation problem for networked Cyber-Physical systems suffering from both disturbances and noise is investigated. In the distributed interval observers, there are some connected interval observers built for the corresponding subsystems. Then, due to the communication burden in [...] Read more.

In this paper, the distributed interval estimation problem for networked Cyber-Physical systems suffering from both disturbances and noise is investigated. In the distributed interval observers, there are some connected interval observers built for the corresponding subsystems. Then, due to the communication burden in Cyber-Physical systems, we consider the case where the communication among distributed interval observers is switching topology. A novel approach that combines

L_{\infty}

methodology with reachable set analysis is proposed to design distributed interval observers. Finally, the performance of the proposed distributed interval observers with switching topology is verified through a simulation example. Full article

(This article belongs to the Special Issue Dynamical System and Stochastic Analysis)

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13 pages, 977 KiB

Open AccessArticle

Combination of Functional and Disturbance Observer for Positive Systems with Disturbances

by Lanai Huang, Xudong Zhao, Fengyu Lin and Junfeng Zhang

Mathematics 2023, 11(1), 200; https://doi.org/10.3390/math11010200 - 30 Dec 2022

Cited by 4 | Viewed by 1376

Abstract

This technique note proposes two classes of functional and disturbance observers for positive systems with structural and non-structural disturbances, respectively. A positive functional observer is first proposed for positive systems by introducing the estimation of disturbance to the observer. By developing the disturbance [...] Read more.

This technique note proposes two classes of functional and disturbance observers for positive systems with structural and non-structural disturbances, respectively. A positive functional observer is first proposed for positive systems by introducing the estimation of disturbance to the observer. By developing the disturbance observer technique, a positive disturbance observer is designed to supply the estimation of disturbance in the functional observer. Then, a new unknown input observer is constructed for positive systems. A matrix decomposition method is employed to design the observer gains. All conditions are described in terms of linear programming. The corresponding algorithms are addressed for computing the presented conditions. Finally, two examples are provided to verify the effectiveness of the theoretical findings. Full article

(This article belongs to the Special Issue Dynamical System and Stochastic Analysis)

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15 pages, 488 KiB

Open AccessArticle

Robust Synchronization of Fractional-Order Chaotic System Subject to Disturbances

by Dongya Li, Xiaoping Zhang, Shuang Wang and Fengxiang You

Mathematics 2022, 10(24), 4639; https://doi.org/10.3390/math10244639 - 7 Dec 2022

Cited by 1 | Viewed by 1079

Abstract

This paper studies the synchronization problem for a class of chaotic systems subject to disturbances. The nonlinear functions contained in the master and slave systems are assumed to be incremental quadratic constraints. Under some assumptions, a feedback law is designed so that the [...] Read more.

This paper studies the synchronization problem for a class of chaotic systems subject to disturbances. The nonlinear functions contained in the master and slave systems are assumed to be incremental quadratic constraints. Under some assumptions, a feedback law is designed so that the error system behaves like the

H^{\infty}

performance. Meanwhile, the detailed algorithm for computing the incremental multiplier matrix is also given. Finally, one numerical example and one practical example are simulated to show the effectiveness of the designed method. Full article

(This article belongs to the Special Issue Dynamical System and Stochastic Analysis)

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19 pages, 1951 KiB

Open AccessArticle

Another Case of Degenerated Discrete Chenciner Dynamic System and Economics

by Sorin Lugojan, Loredana Ciurdariu and Eugenia Grecu

Mathematics 2022, 10(20), 3782; https://doi.org/10.3390/math10203782 - 13 Oct 2022

Viewed by 1183

Abstract

The non-degenerate Chenciner bifurcation of a discrete dynamical system is studied using a transformation of parameters which must be regular at the origin of the parameters (the condition CH.1 of the well-known treatise of Kuznetsov). The article studies a complementary case, where the [...] Read more.

The non-degenerate Chenciner bifurcation of a discrete dynamical system is studied using a transformation of parameters which must be regular at the origin of the parameters (the condition CH.1 of the well-known treatise of Kuznetsov). The article studies a complementary case, where the transformation is no longer regular at the origin, representing a degeneration. Four different bifurcation diagrams appear in that degenerated case, compared to only two in the non-degenerated one. Degeneracy may cause volatility in economics systems modeled by discrete Chenciner dynamical systems. Full article

(This article belongs to the Special Issue Dynamical System and Stochastic Analysis)

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14 pages, 4213 KiB

Open AccessArticle

Stability and Stabilization of 2D Linear Discrete Systems with Fractional Orders Based on the Discrimination System of Polynomials

by Xiaoxue Li, Xiaorong Hou, Jing Yang and Min Luo

Mathematics 2022, 10(11), 1862; https://doi.org/10.3390/math10111862 - 29 May 2022

Cited by 3 | Viewed by 1745

Abstract

This paper considers the stability and stabilization of two-dimensional (2D) fractional-order systems described by state-space model based on the discrimination system of polynomials. Necessary and sufficient conditions of stability and stabilization are established. We change the criterion for checking the stability of linear [...] Read more.

This paper considers the stability and stabilization of two-dimensional (2D) fractional-order systems described by state-space model based on the discrimination system of polynomials. Necessary and sufficient conditions of stability and stabilization are established. We change the criterion for checking the stability of linear discrete-time 2D fractional-order systems into an easy checking criterion whether some polynomials are positive. We use the discrimination system of polynomials to check the new conditions. For the stabilization problem, we get a stable gain matrix region. The unstable system with the gain parameters of the stable gain matrix region is stable. We give the method of stability analysis and stabilization for the general 2D fractional-order system. An example shows the validity of the proposed stability and stabilization methods. Full article

(This article belongs to the Special Issue Dynamical System and Stochastic Analysis)

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17 pages, 2521 KiB

Open AccessArticle

Chenciner Bifurcation Presenting a Further Degree of Degeneration

by Sorin Lugojan, Loredana Ciurdariu and Eugenia Grecu

Mathematics 2022, 10(9), 1603; https://doi.org/10.3390/math10091603 - 8 May 2022

Cited by 1 | Viewed by 1817

Abstract

Chenciner bifurcation appears for some two-dimensional systems with discrete time having two independent variables. Investigated here is a special case of degeneration where the implicit function theorem cannot be used around the origin, so a new approach is necessary. In this scenario, there [...] Read more.

Chenciner bifurcation appears for some two-dimensional systems with discrete time having two independent variables. Investigated here is a special case of degeneration where the implicit function theorem cannot be used around the origin, so a new approach is necessary. In this scenario, there are many more bifurcation diagrams than in the two non-degenerated cases. Several numerical simulations are presented. Full article

(This article belongs to the Special Issue Dynamical System and Stochastic Analysis)

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21 pages, 515 KiB

Open AccessArticle

Event-Triggered Asynchronous Filter of Nonlinear Switched Positive Systems with Output Quantization

by Shitao Zhang, Peng Lin and Junfeng Zhang

Mathematics 2022, 10(4), 599; https://doi.org/10.3390/math10040599 - 15 Feb 2022

Cited by 1 | Viewed by 1934

Abstract

This paper deals with a static/dynamic event-triggered asynchronous filter of nonlinear switched positive systems with output quantization. The nonlinear function is located in a sector. Both static and dynamic event-triggering conditions are established based on the 1-norm form. By virtue of the event-triggering [...] Read more.

This paper deals with a static/dynamic event-triggered asynchronous filter of nonlinear switched positive systems with output quantization. The nonlinear function is located in a sector. Both static and dynamic event-triggering conditions are established based on the 1-norm form. By virtue of the event-triggering mechanism, the error system is transformed into an interval uncertain system. An event-triggered asynchronous filter is designed by employing a matrix decomposition approach. The positivity and

L_{1}

-gain stability of the error system are guaranteed by means of linear copositive Lyapunov functions and a linear programming approach. Finally, two examples are given to verify the effectiveness of the design. Full article

(This article belongs to the Special Issue Dynamical System and Stochastic Analysis)

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Review

Jump to: Research

22 pages, 901 KiB

Open AccessReview

An Overview of Recent Advances in the Event-Triggered Consensus of Multi-Agent Systems with Actuator Saturations

by Jing Xu and Jun Huang

Mathematics 2022, 10(20), 3879; https://doi.org/10.3390/math10203879 - 19 Oct 2022

Cited by 8 | Viewed by 2069

Abstract

The event-triggered consensus of multi-agent systems received extensive attention in academia and industry perspectives since it ensures all agents eventually converge to a stable state while reducing the utilization of network communication resources effectively. However, the practical limitation of the actuator could lead [...] Read more.

The event-triggered consensus of multi-agent systems received extensive attention in academia and industry perspectives since it ensures all agents eventually converge to a stable state while reducing the utilization of network communication resources effectively. However, the practical limitation of the actuator could lead to a saturation phenomenon, which may degrade the systems or even induce instability. This paper plans to offer a detailed review of some recent results in the event-triggered consensus of multi-agent systems subject to actuator saturation. First, the multi-agent system model with actuator saturation constraints is given, and the basic framework of the event-triggering mechanism is introduced. Second, representative results reported in recent valuable papers are reviewed based on methods for dealing with saturated terms, including low-gain feedback, sector-bounded conditions, and convex hull representations. Finally, some challenging topics worthy of research efforts are dicussed for future research. Full article

(This article belongs to the Special Issue Dynamical System and Stochastic Analysis)

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