The aim of this work is to describe the dynamics a discrete fractional-order reaction–diffusion FitzHugh–Nagumo model. We established acceptable requirements for local asymptotic stability system’s unique equilibrium. Moreover, we employed Lyapunov functional show that constant equilibrium solution globally asymptotically stable. Furthermore, numerical simulations are shown clarify and exemplif...

A fractional model of the Hopfield neural network is considered in case application generalized proportional Caputo derivative. The stability analysis this used to show reliability processed information. An equilibrium defined, which generally not a constant (different than ordinary derivatives and Caputo-type derivatives). We define exponential Mittag–Leffler equilibrium. For this, we extend s...

As a complex non-linear system, the chaotic oscillation of power system seriously threatens safe and stable operation grids. In this paper, finite time adaptive synchronization control method is proposed to mitigate problem in system. The can realize chaos parameter identification by completely synchronizing fractional-order with identify parameters within time. fractional Lyapunov stability th...

In this paper, a class of fractional-order symmetric hyperchaotic systems is studied based on the Adomian decomposition method. Starting from definition Adomian, nonlinear term five-dimensional chaotic system decomposed. At same time, dynamic behavior analyzed by using bifurcation diagrams, Lyapunov exponent spectrum, complexity and attractor phase diagrams. The simulation results show that wit...

This article studies the global Mittag-Leffler stability of fractional order fuzzy cellular neural networks via hybrid feedback controllers. Based on control technique Lyapunov approach, and some novel analysis techniques calculation, sufficient conditions are obtained to guarantee Global Mittag-Lefflers stability. Finally, two simulation example given illustrate effectiveness proposed method.

Chaotic oscillation will occur in power system when there exist periodic load disturbances. In order to analyze the chaotic characteristics and suppression method, this paper establishes simplified mathematical model of interconnected two-machine analyzes nonlinear dynamic behaviors, such as phase diagram, dissipation, bifurcation map, spectrum, Lyapunov exponents. Based on fractional calculus ...

Recommended by Jianshe Yu It is supposed that the fractional difference equation xn 1 μ ∑k j 0ajxn−j / λ ∑k j 0bjxn−j , n 0, 1, . . . , has an equilibrium point x̂ and is exposed to additive stochastic perturbations type of σ xn − x̂ ξn 1 that are directly proportional to the deviation of the system state xn from the equilibrium point x̂. It is shown that known results in the theory of stability o...

This paper proposes a novel sliding mode control (SMC) scheme to stabilize a class of fractional-order chaotic systems. Through constructing two sliding mode variables, the control problem of n-dimensional system can be transformed to the equivalent stabilizing problem of a reduced-order system. Subsequently, on the basis of second-order sliding mode (SOSM) technique, a robust control law is de...

This paper deals with chaos synchronization between two different uncertain fractional order chaotic systems based on adaptive fuzzy sliding mode control (AFSMC). With the definition of fractional derivatives and integrals, a fuzzy Lyapunov synthesis approach is proposed to tune free parameters of the adaptive fuzzy controller on line by output feedback control law and adaptive law. Moreover, c...

We use the variational approach to investigate periodic measures for a class of stochastic partial differential equations (SPDEs) with regime-switching. The hybrid system is driven by degenerate Lévy noise. Lyapunov function method study existence and show uniqueness establishing strong Feller property irreducibility associated time-inhomogeneous semigroup. main results are applied fractional p...