Mohd Salmi Md Noorani

Regular Generalized ω-Closed Sets

In 1982 and 1970, Hdeib and Levine introduced the notions of ω-closed set and generalized closed set, respectively. The aim of this paper is to provide a relatively new notion of generalized closed set, namely, regular generalized ω-closed, regular generalized ω-continuous, a-ω-continuous, and regular generalized ω-irresolute maps and to study its fundamental properties.

Approximate analytical solutions of systems of PDEs by homotopy analysis method

In this paper, the homotopy analysis method (HAM) is applied to obtain series solutions to linear and nonlinear systems of first- and second-order partial differential equations (PDEs). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of series solutions. It is shown in particular that the solutions obtained by the variational iteration method (VIM) are only special cases of the HAM solutions.

Numerical simulation of the generalized Huxley equation by He's variational iteration method

Abstract By means of variational iteration method the solution of generalized Huxley equation are obtained, comparison with the Adomian decomposition method is made, showing that the former is more effective than the later. In this paper, He’s variational iteration method is introduced to overcome the difficulty arising in calculating Adomian polynomials.

A note on the Adomian decomposition method for the generalized Huxley equation

In a recent paper, Ismail et al. [Adomian decomposition method for Burgers-Huxley and Burgers-Fisher equations, Appl. Math. Comput. 159 (2004) 291-301] employed the Adomian decomposition method (ADM) to solve, in particular, a generalized nonlinear Huxley equation. The purpose of this note is to correct Ismail et al.s numerical solutions of the generalized Huxley equation. In addition, a convergence proof of the ADM applied to the generalized Huxley equation is also given.

Projective lag synchronization in drive-response dynamical networks

This paper investigates projective lag synchronization (PLS) behavior between chaotic systems in drive-response dynamical networks (DRDNs) model with nonidentical nodes. A hybrid feedback control method is designed to achieve the PLS with and without mismatched terms. Specially, the coupling matrix in this model is not assumed to be symmetric, diffusive or irreducible. The stability of the error dynamics is proven theoretically using the Lyapunov stability theory. Finally, analytical results show that the states of the dynamical network with non-delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Moreover, the numerical simulations results demonstrate the validity of the proposed method.

Contra-ω-Continuous and Almost Contra-ω-Continuous

The notion of contra continuous functions was introduced and investigated by Dontchev. In this paper, we apply the notion of ω-open sets in topological space to present and study a new class of called almost contra ω-continuous functions as a new generalization of contra continuity.

Fixed Point Results in Quasi-Cone Metric Spaces

The main aim of this paper is to prove fixed point theorems in quasi-cone metric spaces which extend the Banach contraction mapping and others. This is achieved by introducing different kinds of Cauchy sequences in quasi-cone metric spaces.

Exact solutions of equation generated by the jaulent-miodek hierarchy by (G'/G)-expansion method

The -expansion method is proposed for constructing more general exact solutions of the nonlinear -dimensional equation generated by the Jaulent-Miodek Hierarchy. As a result, when the parameters are taken at special values, some new traveling wave solutions are obtained which include solitary wave solutions which are based from the hyperbolic functions, trigonometric functions, and rational functions. We find in this work that the -expansion method give some new results which are easier and faster to compute by the help of a symbolic computation system. The results obtained were compared with tanh method.

Analysis of a New Quadratic 3D Chaotic Attractor

A new three-dimensional chaotic system is introduced. Basic properties of this system show that its corresponding attractor is topologically different from some well-known systems. Next, detailed information on dynamic of this system is obtained numerically by means of Lyapunov exponents spectrum, bifurcation diagrams, and 0-1 chaos indicator test. We finally prove existence of this chaotic attractor theoretically using Shil’nikov theorem and undetermined coefficient method.

Adaptive projective lag synchronization of uncertain complex dynamical networks with disturbance

Projective lag synchronization behavior with non-delay and delay coupling in complex dynamical network model is investigated in this paper. Based on Lyapunov stability theory, adaptive control scheme is applied to achieve the projective lag synchronization model with identical, different nodes and even if the delay coupling have constant time delay or time-varying coupling delay. In addition, the model consists of disturbances and fully unknown parameters. Theses parameters are identified by adaptive control and update law. Finally, the simulation results reveal that the states of the dynamical network with non-delay and delay coupling can be asymptotically synchronized onto a desired scaling under the designed controller. Additionally, numerical examples demonstrate the effectiveness of the proposed method.