Abstract
This paper is devoted to introduce a novel fourth-order hyperchaotic system. The hyperchaotic system is constructed by adding a linear feedback control level based on a modified Lorenz-like chaotic circuit with reduced number of amplifiers. The local dynamical entities, such as the basic dynamical behavior, the divergence, the eigenvalue, and the Lyapunov exponents of the new hyperchaotic system, are all investigated analytically and numerically. Then, an active control method is derived to achieve global chaotic synchronization of the novel hyperchaotic system through making the synchronization error system asymptotically stable at the origin based on Lyapunov stability theory. Next, the proposed novel hyperchaotic system is applied to construct another new hyperchaotic system with circuit deformation and design a new hyperchaotic secure communication circuit. Furthermore, the implementation of two novel electronic circuits of the proposed hyperchaotic systems is presented, examined, and realized using physical components. A good qualitative agreement is shown between the simulations and the experimental results around 500 kHz and below 1 MHz.
Highlights
The Lorenz chaotic system was proposed [1] and later the chaotic synchronization was implemented in the electronic circuit [2], which greatly inspired many scientists and accelerated the pace of chaos research [3,4,5,6,7]
The contribution of this paper is that we introduce a novel fourth-order hyperchaotic system on the basis of a modified Lorenz-like chaotic circuit with reduced number of Complexity amplifiers
A novel hyperchaotic system is proposed based on a modified Lorenz-like chaotic circuit with reduced number of amplifiers
Summary
The Lorenz chaotic system was proposed [1] and later the chaotic synchronization was implemented in the electronic circuit [2], which greatly inspired many scientists and accelerated the pace of chaos research [3,4,5,6,7]. Mahmoud et al introduced some chaotic and hyperchaotic systems with complex variables, analyzed their chaotic behavior, and proposed several types of synchronization methods [20,21,22,23,24,25]. The contribution of this paper is that we introduce a novel fourth-order hyperchaotic system on the basis of a modified Lorenz-like chaotic circuit with reduced number of Complexity amplifiers. The analog circuit implementation results match the Multisim and Matlab simulation results These proposed circuit design methods can be applied in other complex hyperchaotic systems.
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