M.S.M. Noorani

Adaptive anti-synchronization of chaotic systems with fully unknown parameters

This paper centers on the chaos anti-synchronization between two identical or different chaotic systems using adaptive control. The sufficient conditions for achieving the anti-synchronization of two chaotic systems are derived based on Lyapunov stability theory. An adaptive control law and a parameter update rule for unknown parameters are introduced such that the Chen system is controlled to be the Lorenz system. Theoretical analysis and numerical simulations are shown to verify the results.

The multistage variational iteration method for a class of nonlinear system of ODEs

This paper implements the multistage variational iteration method (MVIM) to solve a class of nonlinear system of first-order ordinary differential equations (ODEs). The domain of validity of the solutions via the standard variational iteration method (VIM) is extended by the simple multistage strategy. Comparisons with the exact solution and the fourth-order Runge–Kutta (RK4) method show that the MVIM is a reliable method for nonlinear equations.

Adaptive reduced-order anti-synchronization of chaotic systems with fully unknown parameters

Article history: Received 17 February 2009 Received in revised form 31 October 2009 Accepted 1 November 2009 Available online 10 November 2009

Variational iteration method for solving multispecies Lotka-Volterra equations

This paper applies the variational iteration method to multispecies Lotka-Volterra equations. Comparisons with the Adomian decomposition and the fourth-order Runge-Kutta methods show that the variational iteration method is a powerful method for nonlinear equations.

Chaos Anti-synchronization between Two Novel Different Hyperchaotic Systems

We demonstrate that anti-synchronization can coexist in two different hyperchaotic systems of ratchets moving in different asymmetric potentials by active control method. By using rigorous mathematical theory, the sufficient condition is drawn for the stability of the error dynamics, where the controllers are designed by using the sum of the relevant variables in hyperchaotic systems. Numerical results are presented to justify the theoretical analysis strategy.

Adaptive Increasing-Order Synchronization and Anti-Synchronization of Chaotic Systems with Uncertain Parameters

We elaborate the concept of increasing-order synchronization and anti-synchronization of chaotic systems via an adaptive control scheme and modulation parameters. It is shown that the dynamical evolution of a third-order chaotic system can be synchronized and anti-synchronized with a fourth-order chaotic system even though their parameters are unknown. Theoretical analysis and numerical simulations are carried out to verify the results.

Solutions of Heat-Like and Wave-Like Equations with Variable Coefficients by Means of the Homotopy Analysis Method

We employ the homotopy analysis method (HAM) to obtain approximate analytical solutions to the heat-like and wave-like equations. The HAM contains the auxiliary parameter ħ, which provides a convenient way of controlling the convergence region of series solutions. The analysis is accompanied by several linear and nonlinear heat-like and wave-like equations with initial boundary value problems. The results obtained prove that HAM is very effective and simple with less error than the Adomian decomposition method and the variational iteration method.

Homotopy approach for the hyperchaotic Chen system

In this paper, the numerical–analytical solution for the hyperchaotic Chen system is obtained via the multistage homotopy analysis method (MSHAM). An analytical form of the solution within each time interval is given, which is not possible using standard numerical methods. The numerical results obtained by the MSHAM and the classical fourth-order Runge–Kutta (RK4) method are in complete agreement. Moreover, the residual error for the MSHAM solution is given for each time interval.

Active Anti-Synchronization Between Identical and Distinctive Hyperchaotic Systems

This paper brings attention to hyperchaos anti-synchronization between two identical and distinctive hyperchaotic systems using active control theory. The sufficient conditions for achieving anti-synchronization of two high dimensional hyperchaotic systems is derived based on Lyapunov stability theory, where the controllers are designed by using the sum of relevant variables in hyperchaotic systems. Numerical results are presented to justify the theoretical analysis strategy.

Anti-Synchronization of Chaotic Systems via Adaptive Sliding Mode Control

An anti-synchronization scheme is proposed to achieve the anti-synchronization behavior between chaotic systems with fully unknown parameters. A sliding surface and an adaptive sliding mode controller are designed to gain the anti-synchronization. The stability of the error dynamics is proven theoretically using the Lyapunov stability theory. Finally numerical results are presented to justify the theoretical analysis.