Analytical study of global bifurcations,stabilization and chaos synchronization of jerk system with multiple attractors

Nonlinear Dynamics - This paper investigates the fixed-time synchronization of complex dynamical networks with nonidentical nodes in the presence of bounded uncertainties and disturbances using...     

Complex dynamics of a discrete fractional‐order Leslie‐Gower predator‐prey model

A proposed discretized form of fractional‐order prey‐predator model is investigated. A sufficient condition for the solution of the discrete system to exist and to be unique is determined. Jury stability test is applied for studying stability of equilibrium points of the discretized system. Then, the effects of varying fractional order and other parameters of the systems on its dynamics are examined. The system undergoes Neimark‐Sacker and flip bifurcation under certain conditions. We observe that the model exhibits chaotic dynamics following stable states as the memory parameter α decreases and step size h increases. Theoretical results illustrate the rich dynamics and complexity of the model. Numerical simulation validates theoretical results and demonstrates the presence of rich dynamical behaviors include S‐asymptotically bounded periodic orbits, quasi‐periodicity, and chaos. The system exhibits a wide range of dynamical behaviors for fractional‐order α key parameter.     

Further nonlinear dynamical analysis of simple jerk system with multiple attractors

Nonlinear Dynamics - This paper presents an analytical framework to investigate the dynamical behavior of a recent chaotic jerk model with multiple attractors. The methods of analytical analysis...     

Dynamical behavior,chaos control and synchronization of a memristor-based ADVP circuit

This paper is devoted to study the dynamical behavior of a modified Autonomous Van der Pol-Duffing (ADVP) circuit when its nonlinear element is replaced by a flux controlled memristor. The bifurcation diagrams, Lyapunov exponents, and phase portraits of the state variables are presented. Then, the chaos which appears at certain values of the system’s parameters is controlled using linear feedback control. Finally, the synchronization between two chaotic modified ADVP circuits is achieved in the case of fully unknown parameters of the system using adaptive synchronization.     

Numerical simulation and stability analysis of a novel reaction–diffusion COVID-19 model

Nonlinear Dynamics - In this study, a novel reaction–diffusion model for the spread of the new coronavirus (COVID-19) is investigated. The model is a spatial extension of the recent COVID-19...     

Synchronization of different dimensional chaotic systems with time varying parameters, disturbances and input nonlinearities

In this paper, the problems of robust exponential generalized and robust exponential Q-S chaos synchronization are investigated between different dimensional chaotic systems. We consider the more practical and realistic cases when unknown time varying parameters with uncertainties, environmental disturbances, and nonlinearity of input control signals are present. The adaptive technique is employed to design the appropriate controllers and the validity of the proposed controllers are proved using Lyapunov stability theorem. Furthermore, numerical simulations are performed to show the efficiency of the presented scheme.