Azizan Bin Saaban

Global chaos synchronization of new chaotic system using linear active control

Chaos synchronization is a procedure where one chaotic oscillator is forced to adjust the properties of another chaotic oscillator for all future states. This research paper studies and investigates the global chaos synchronization problem of two identical chaotic systems and two non-identical chaotic systems using the linear active control technique. Based on the Lyapunov stability theory and using the linear active control technique, the stabilizing controllers are designed for asymptotically global stability of the closed-loop system for both identical and non-identical synchronization. Numerical simulations and graphs are imparted to justify the efficiency and effectiveness of the proposed scheme. All simulations have been done by using mathematica 9.

A Research on Active Control to Synchronize a New 3D Chaotic System

This paper presents the robust synchronization problem of a 3D chaotic system by using the active control technique. Based on the Gershgorin theorem and Routh-Hurwitz criterion, sufficient algebraic conditions are derived to design a linear controller gain matrix. The conditions are then applied for the robust stability of the synchronization error dynamics in the presence of an unknown bounded smooth external disturbance. The proposed active control strategy with a suitable computation of the linear controller gain matrix is simple in design and establishes fast convergence rates of the synchronization error signals. Numerical simulation results further verified the analytical results.

Complete synchronization of uncertain chaotic systems via a single proportional adaptive controller: A comparative study

This paper addresses a comparative computational study on the synchronization quality, cost and converging speed for two pairs of identical chaotic and hyperchaotic systems with unknown time-varying parameters. It is assumed that the unknown time-varying parameters are bounded. Based on the Lyapunov stability theory and using the adaptive control method, a single proportional controller is proposed to achieve the goal of complete synchronizations. Accordingly, appropriate adaptive laws are designed to identify the unknown time-varying parameters. The designed control strategy is easy to implement in practice. Numerical simulations results are provided to verify the effectiveness of the proposed synchronization scheme.

Local stability condition of the equilibrium of an oligopoly market with bounded rationality adjustment

This paper considers an n-firm oligopoly market where each firm produces a single homogenous product under a constant unit cost. Nonlinearity is introduced into the model of this oligopoly market by assuming the market has an isoelastic demand function. Furthermore, instead of the usual assumption of perfectly rational firms, they are assumed to be boundedly rational in adjusting their outputs at each period. The equilibrium of this n discrete dimensional system is obtained and its local stability is calculated.

The structure of a market containing boundedly rational firms

The structure of a market is determined by the number of active firms in it. Over time, this number is affected by the exit of existing firms, called incumbents, and entries of new firms, called entrant. In this paper, we considered a market governed by the Cobb-Douglas utility function such that the demand function is isoelastic. Each firm is assumed to produce a single homogenous product under a constant unit cost. Furthermore, firms are assumed to be boundedly rational in adjusting their outputs at each period. A firm is considered to exit the market if its output is negative. In this paper, the market is assumed to have zero barrier-to-entry. Therefore, the exiting firm can reenter the market if its output is positive again, and new firms can enter the market easily. Based on these assumptions and rules, a mathematical model was developed and numerical simulations were run using Matlab. By setting certain values for the parameters in the model, initial numerical simulations showed that in the long run...

Series solution of fuzzy linear Cauchy reaction-diffusion equation by using homotopy perturbation method

In this study, Homotopy Perturbation Method (HPM) is proposed, analyzed and developed to solve the fuzzy linear Cauchy reaction-diffusion equation with the fuzzy initial condition. HPM allows for the solution of the fuzzy linear Cauchy reaction-diffusion problem be calculated in the form of series function in which the ingredient can be easily determined and it will be constructed and formulated by using the properties of fuzzy set theory. A numerical experiment is investigated to verify convergence results for comparative purpose with the analytical solution of the given problem to illustrate the efficacy and the capability of the proposed method.

Numerical solution of second-order fuzzy nonlinear two-point boundary value problems using combination of finite difference and Newton’s methods

In this paper, we discuss the numerical solution of second-order nonlinear two-point fuzzy boundary value problems (TPFBVP) by combining the finite difference method with Newton’s method. Numerical example using the well-known nonlinear TPFBVP is presented to show the capability of the new method in this regard and the results are satisfied the convex triangular fuzzy number. We also compare the numerical results with the exact solution, and it shows that the proposed method is good approximation for the analytic solution of the given TPFBVP.

Notes on multidimensional fixed-point theorems

Abstract In this paper we prove the existence and uniqueness of coincident (fixed) points for nonlinear mappings of any number of arguments under a (ψ, θ, φ)-weak contraction condition without O-compatibility. The obtained results extend, improve and generalize some well-known results in the literature to be discussed below. Moreover, we present an example to show the efficiency of our results.

Improved Time Response of Stabilization in Synchronization of Chaotic Oscillators Using Mathematica

Chaotic dynamics are an interesting topic in nonlinear science that has been intensively studied during the last three decades due to its wide availability. Motivated by much researches on synchronization, the authors of this study have improved the time response of stabilization when parametrically excited Φ6—Van der Pol Oscillator (VDPO) and Φ6—Duffing Oscillator (DO) are synchronized identically as well as non-identically (with each other) using the Linear Active Control (LAC) technique using Mathematica. Furthermore, the authors have synchronized the same pairs of the oscillators using a more robust synchronization with faster time response of stability called Robust Adaptive Sliding Mode Control (RASMC). A comparative study has been done between the previous results of Njah’s work and our results based on Mathematica via LAC. The time response of stabilization of synchronization using RASMC has been discussed.