Abstract
A new four-dimensional hyperchaotic system is investigated. Numerical and analytical studies are carried out on its basic dynamical properties, such as equilibrium point, Lyapunov exponents, Poincaré maps, and chaotic dynamical behaviors. We verify the realizability of the new system via an electronic circuit by using Multisim software. Furthermore, a generalized function projective synchronization scheme of two different hyperchaotic systems with uncertain parameters is proposed, which includes some existing projective synchronization schemes, such as generalized projection synchronization and function projective synchronization. Based on the Lyapunov stability theory, a controller with parameters update laws is designed to realize synchronization. Using this controller, we realize the synchronization between Chen hyperchaotic system and the new system to verify the validity and feasibility of our method.
Highlights
Chaos is a very fascinating nonlinear phenomenon, which exhibits extreme sensitivity to initial conditions and has noise-like behaviors
The generalized function projective synchronization (GFPS) of Chen hyperchaotic system and the proposed hyperchaotic system is considered as an example; the simulation results of this example verify the validity of our method
The controller for GFPS based on Lyapunov stability theory is put forward, and simulation results of an example are provided to realize the synchronization between Chen hyperchaotic system and the new system
Summary
Chaos is a very fascinating nonlinear phenomenon, which exhibits extreme sensitivity to initial conditions and has noise-like behaviors. In [27], a modified projective synchronization (MPS) scheme was investigated, in which the dynamical states of the drive system and response system synchronized up to a constant scaling matrix. In [29], Du et al introduced a modified function projective synchronization (MFPS) of chaotic system, where the dynamical states of the drive and response system can be synchronized up to a desired scaling function matrix. In [36], Yu et al further proposed a generalized function projective synchronization (GFPS) of two different chaotic systems with fully unknown parameters. The controller for GFPS based on Lyapunov stability theory is put forward, and simulation results of an example are provided to realize the synchronization between Chen hyperchaotic system and the new system .
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