Magnetic-liquid double-suspension bearing (MLDSB) is composed of an electromagnetic supporting system and a hydrostatic supporting system. Due to its greater supporting capacity and stiffness, it is appropriate for middle-speed applications, overload...
The purpose of the present paper is to study the presence of bifurcations of zero-Hopf type at a generalized Genesio differential equation. More precisely, by transforming such differential equation in a first-order differential system in the three-d...
This paper presents a two-dimensional simplified Hodgkin–Huxley model under exposure to electric fields. The Hopf bifurcations of the simplified Hodgkin–Huxley model are investigated through qualitative analysis and numerical simulations....
This paper investigates the dynamical characteristics of the Boissonade model in a class of reaction–diffusion chemical systems with time delays, analyzing the system’s Hopf bifurcation with time delay as the parameter under both diffusio...
Here we study 3-dimensional Lotka–Volterra systems. It is known that some of these differential systems can have at least four periodic orbits bifurcating from one of their equilibrium points. Here we prove that there are some of these differen...
A differential equation of panel vibration in supersonic flow is established on the basis of the thin-plate large deflection theory under the assumption of a quasi-steady temperature field. The equation is dimensionless, and the derivation of its sec...
This paper investigates stability switches induced by Hopf bifurcation in a fractional three-neuron network that incorporates both neutral time delay and communication delay, as well as a general structure. Initially, we simplified the characteristic...
This study proposes a mathematical model that accounts for the interaction of bacteria, phages, and the innate immune response with a discrete time delay. First, for the non-delayed model we determine the local and global stability of various equilib...
The distribution of nutrients and microorganisms in sediments is not uniform, as it results from the complex interactions between chemical, biological, and physical transport processes. This study investigates, through a simplified model, the dynamic...
Under the background of double carbon, it is important to study forest pests and diseases to improve forest carbon sink. In this paper, we establish a delayed model associated with the larvae and adults of Saperda populnea, susceptible poplars, and i...
In this paper, a delayed reaction–diffusion equation with carrying capacity-driven diffusion is investigated. The stability of the positive equilibrium solutions and the existence of the Hopf bifurcation of the equation are considered by studyi...
This article first studies the stability conditions of a Chua system depending on six parameters. After, using the averaging method, as well as the methods of the Gröbner basis and real solution classification, we provide sufficient conditions f...
In this work, a Lotka–Volterra type predator–prey system with time delay and stage structure for the predators is proposed and analyzed. By using the permanence theory for infinite dimensional system, we get that the system is permanent i...
In this paper, we studied a nutrient–phytoplankton model with time delay and diffusion term. We studied the Turing instability, local stability, and the existence of Hopf bifurcation. Some formulas are obtained to determine the direction of the...
This paper investigates the effect of a gene expression time delay on the Brusselator model with reaction and diffusion terms in one dimension. We obtain ODE systems analytically by using the Galerkin method. We determine a condition that assists in...
In this paper, a new four-dimensional (4D) hyperchaotic biplane system is designed and presented. The dynamical properties of this new system are studied by means of tools such as bifurcation diagrams, Lyapunov exponents and phase diagrams. The Hopf...
In this paper, we study the stability and Hopf bifurcation of a class of six-neuron fractional BAM neural networks with multiple delays. Firstly, the model is transformed into a fractional neural network model with two nonidentical delays by using va...
This paper mainly studies the equivariant Hopf bifurcation of a delayed reaction–diffusion predator–prey model with stage structures on a two-dimensional circular domain. Firstly, we calculate the existence of steady-state solutions, and...
We consider a duopoly game model of R&D (research and development) rivalry between two high-tech firms with time delay, in which a monopoly sector with R&D spillover is studied using a mixture of game theory and nonlinear dynamics theory. The...
Analysis and controlling of bifurcation for a class of chaotic Van der Pol- Duffing system with multiple unknown parameters are conducted. The stability of the equilibrium of the system is studied by using Routh-Hurwitz criterion, and the critical va...
To reveal the nonlinear instability mechanism by which the three-degree-of-freedom rotor system of a magnetic-liquid double suspension bearing transforms from stable suspension to periodic vibration, a nonlinear dynamic model considering electromagne...
In this study, we examine the effectiveness of combining interleukin-2 (IL-2) with highly active antiretroviral therapy (HAART) in controlling HIV replication. A mathematical model of the immune system is developed to analyze immune recovery when IL-...
In this paper, a diffusive predator–prey model with a memory effect in predator and anti-predator behaviour in prey is studied. The stability of the coexisting equilibrium and the existence of Hopf bifurcation are analysed by analysing the dist...
This study models the subcritical Hopf bifurcation in thermoacoustic Stirling engines using the Stuart–Landau model, highlighting the role of nonlinear dynamics. By inducing self-sustained oscillations and measuring pressure fluctuations across...
This paper investigates the Hopf-like bifurcation of a fractional tumor-lymphatic model with two time delays. The two time delays are considered as branching parameters, and we analyze their influences on the dynamic properties of the model. Through...
This paper investigates the complex dynamics of a ratio-dependent predator–prey model incorporating the Allee effect in prey and predator harvesting. To explore the joint effect of the harvesting effort and diffusion on the dynamics of the syst...
The purpose of this paper is to study a predator–prey model with Allee effect and double time delays. This research examines the dynamics of the model, with a focus on positivity, existence, stability and Hopf bifurcations. The stability of the...
The propagation of rumors on online social networks (OSNs) brings an awful lot of trouble to people’s life and society. Aiming at combating rumors spreading on OSNs, two novel rumor-propagation models without and with time delays are proposed,...
In this paper, the stability and Hopf bifurcation of fractional-order quaternion-valued neural networks (FOQVNNs) with various types of time delays are studied. The fractional-order quaternion neural networks with time delays are decomposed into an e...
In this paper, we investigate the nonlinear dynamic behavior of a cart–double pendulum system with single time delay feedback control. Based on the center manifold theorem and stochastic averaging method, a reduced-order dynamic model of the sy...
In this paper, we propose and analyze a three-dimensional fractional predator–prey system with two nonidentical delays. By choosing two delays as the bifurcation parameter, we first calculate the stability switching curves in the delay plane. B...
In this paper, we investigate the asymptotic behavior of solutions to a diffusive forest kinematic model, which describes the interactions among young trees, old trees, and airborne seeds. Our study focuses on the stability of the positive equilibriu...
This paper proposes a diffusive predator–prey model with double time delays and prey refuge, incorporating an additive Allee effect. First, we analyze the stability of boundary equilibrium, and the impact of Allee effect on the stability at bou...
Dysbiosis of the gut microbiota and dysregulated immune responses are key pathological features in both the onset and progression of Crohn’s disease. We propose a phagocyte–bacteria diffusion model with a time delay to explore their dynam...
The present work provides a detailed discussion of the dynamical behavior of the delay-induced model of cumulative concentration of hot pollutants, including the contribution of the time-delay parameter to the system’s stability. Analytical res...
This paper studies new energy adoption using a tripartite evolutionary game involving government incentives, enterprise investment, and user adoption. Two time delays are introduced to describe delayed enterprise responses to policy incentives and de...
With the widespread adoption of internet technology globally, the propagation of rumors on social networks has attracted significant scholarly attention. This paper discusses a type of fractional-order rumor propagation model incorporating a saturati...
In order to maximize benefits, oligopolistic competition often occurs in contemporary society. Establishing the mathematical models to reveal the law of market competition has become a vital topic. In the current study, on the basis of the earlier pu...
In this paper, we carry out some research on a predator–prey system with maturation delay, a stage structure for generalist predators and a Holling type-II functional response, which has already been proposed. First, for the delayed model, we o...
In this essay, we introduce a bioeconomic predator–prey model which incorporates the square root functional response and nonlinear prey harvesting. Due to the introduction of nonlinear prey harvesting, the model demonstrates intricate dynamic b...
A generalized delay stage structure prey-predator model with fear effect and prey refuge is considered in this paper via introducing fractional-order and fear effect induced by immature predators. Hopf bifurcation and control of this system are inves...
In this article, we formulated a mathematical model to describe SARS-CoV-2 development in humans, accounting for the dynamics of susceptible and infected epithelial cells, viral particles, ACE2 receptors, cytotoxic T lymphocytes (CTLs), and antibodie...
This paper studies the effects of resource limitations, immunity decay, and delays on an Ebola epidemic model and an optimal control strategy. The model includes two types of delays: a delay in the incubation period of infected individuals and a dela...
Complex nonlinear dynamical systems, often associated with high-entropy time series, have been widely employed to describe and predict intricate dynamic phenomena in real-world systems. Motivated by the need to better understand such complex dynamics...
In this article, we propose a new fractional-order delay-coupled FitzHugh–Nagumo neural model. Taking advantage of delay as a bifurcation parameter, we explore the stability and bifurcation of the formulated fractional-order delay-coupled FitzH...
The doubly-fed variable speed pumped storage unit is a storage system suitable for joint operation with renewable energy sources to smooth the imbalance between renewable energy supply and electricity demand. However, its working principle and operat...
Hydro-wind-solar hybrid power systems have become a mainstream configuration for new-type power systems. However, the high proportion of power-electronics-interfaced generation alters system inertia and damping characteristics, leading to complex hig...
Vector-borne diseases, being one of the most difficult infectious diseases to understand, model, and control, account for a large proportion of human infectious diseases. In the current transmission process of infectious diseases, the latent period o...
In this paper, we propose a diffusive predator–prey model with a strong Allee effect and nonlocal competition in the prey and a fear effect and gestation delay in the predator. We mainly study the local stability of the coexisting equilibrium a...
Adaptive feedback can destabilize a loop that would be stable under any fixed gain, so the speed at which the gain adapts is itself a design parameter. We study this effect in a minimal three-dimensional model motivated by the photocatalytic degradat...
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