Chaotic Systems In Finite Time Research Articles

Finite-time synchronization of different dimensional chaotic systems with uncertain parameters and external disturbances

This paper proposes a new control scheme using two scaling matrices that realizes the finite-time synchronization of different-dimensional chaotic systems with parameter uncertainties and external disturbances. Firstly, based on Lyapunov stability theorem and finite-time stability theorem, the definition of finite-time synchronization of chaotic systems with different dimensions is introduced. Secondly, in the case of external disturbance and parameter uncertainty, an adaptive feedback hybrid controller and parameter adaptive laws are designed to synchronize different dimensional uncertain chaotic systems in finite-time. Then, according to the characteristics of the unknown parameters of the system, a transformation matrix is constructed to meet the needs of chaotic systems with different dimensions, and a simplified synchronization control scheme is designed. Finally, two numerical experiments are carried out to verify the effectiveness of the proposed methods.

Finite-time synchronization for chaotic neural networks with stochastic disturbances

In this paper, we focus on the problem of synchronization for chaotic neural networks with stochastic disturbances. Firstly, we provide a basic result that the systems including the drive system, response system, and error system have a unique solution on the whole time horizon. Based on this result, we design a new control law such that the response system can be synchronized with the drive chaotic system in finite time. Furthermore, we show that the settling time is independent of the initial data under some proper conditions, which hints that the fixed-time synchronization of chaotic neural networks can be realized by our proposed method. Finally, we give simulations to verify the theoretical analysis for our main results.

Finite-time synchronization analysis for general complex dynamical networks with hybrid couplings and time-varying delays

This paper focuses on the finite-time synchronization problem for a kind of general complex networks with intrinsic time-varying delays and hybrid couplings (i.e., containing current-state couplings and time-varying delay couplings). By designing a simple discontinuous state feedback controller and using strict analytical techniques, several synchronization criteria are proposed to guarantee that the complex dynamical networks can be synchronized onto an isolated chaotic system in finite time. Besides, the upper bound of the synchronization time could be estimated, which is dependent on the initial values of the system as well as the delays. Then, some finite-time synchronization criteria about special cases of the complex networks are also obtained. Here, the coupling configuration matrices are not required to be symmetric or irreducible in all cases. Finally, numerical examples are provided to demonstrate the correctness of our theoretical results.

Finite-time synchronization of chaotic systems with noise perturbation

In this paper, we investigate the finite-time stochastic synchronization problem of two chaotic systems with noise perturbation. We propose new adaptive controllers, with which we can synchronize two chaotic systems in finite time. Sufficient conditions for the finite-time stochastic synchronization are derived based on the finite-time stability theory of stochastic differential equations. Finally, some numerical examples are examined to demonstrate the effectiveness and feasibility of the theoretical results.

Robust Finite-Time Stabilization of Fractional-Order Chaotic Systems based on Fractional Lyapunov Stability Theory

This paper concerns the problem of stabilization of uncertain fractional-order chaotic systems in finite time. On the basis of fractional Lyapunov stability theory, a robust finite-time fractional controller is introduced to control chaos of fractional-order chaotic systems in the presence of system uncertainties. The finite-time stability of the closed-loop system is analytically proved. An estimation of the convergence time is also given. Some numerical simulations are provided to illustrate the usefulness and applicability of the proposed robust finite-time control approach. It is worth noting that the proposed fractional control method is applicable for stabilizing a broad range of uncertain fractional-order nonlinear systems in a given finite time.