Abstract
Hyperchaotic systems are chaotic systems having more than one positive Lyapunov exponent and they have important applications in secure data transmission and communication. This paper applies active control method for the synchronization of identical and different hyperchaotic Pang systems (2011) and hyperchaotic Wang-Chen systems (2008). Main results are proved with the stability theorems of Lypuanov stability theory and numerical simulations are plotted using MATLAB to show the synchronization of hyperchaotic systems addressed in this paper.
Highlights
Hyperchaotic systems have a lot of important applications in several fields in Science and Engineering
This paper focuses upon active controller design for the anti-synchronization of hyperchaotic Pang systems ([23], 2011) and hyperchaotic Wang-Chen systems ([24], 2008)
Theorem 4.1 The nonlinear controller defined by Eq (18) achieves global and exponential antisynchronization of the identical hyperchaotic Pang systems (14) and (15) for all initial conditions x(0), y(0) ∈ R4
Summary
Hyperchaotic systems have a lot of important applications in several fields in Science and Engineering. They are chaotic systems with more than one positive Lyapunov exponent. This paper focuses upon active controller design for the anti-synchronization of hyperchaotic Pang systems ([23], 2011) and hyperchaotic Wang-Chen systems ([24], 2008). The main results derived in this paper were proved using Lyapunov stability theory [25]. New results have been derived for the anti-synchronization of identical hyperchaotic Pang systems, identical hyperchaotic Wang-Chen systems and non-identical hyperchaotic Pang and hyperchaotic Wang-Chen systems. Numerical simulations were shown using MATLAB to illustrate the main results derived in this paper
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