College of Graduate Studies: Theses & Dissertations

Term of Award

Spring 2014

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (restricted to Georgia Southern)

Copyright Statement / License for Reuse

Digital Commons@Georgia Southern License

Department

Department of Mathematical Sciences

Committee Chair

Yan Wu

Committee Member 1

Jiehua Zhu

Committee Member 2

Alex Stokolos

Abstract

This paper presents algorithms developed in MATLAB to simulate the hyperchaotic Chen system and also estimates the largest Lyapunov characteristic exponent (LCE) and provides a method to compute the entire Lyapunov spectrum of the dynamical system. The computation of the Lyapunov spectrum relies on calculating the order-p LCEs and repeated application of the Gram-Schmidt orthonormalization procedure. We expect two positive LCEs for the Chen System. The program is adaptive to any n-th order chaotic and hyperchaotic systems. Controllers are then developed in order to stablize the hyperchaotic Chen system via linear feedback, speed feedback and nonlinear feedback control and a stability analysis is presented.

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