Abstract
Exploring the dynamics feature of robust chaotic system is an attractive yet recent topic of interest. In this paper, we introduce a three-dimensional fractional-order chaotic system. The important finding by analysis is that the position of signalx3descends at the speed of 1/cas the parameterbincreases, and the signal amplitude ofx1,x2can be controlled by the parametermin terms of the power function with the index −1/2. What is more, the dynamics remains constant with the variation of parametersbandm. Consequently, this system can provide rich encoding keys for chaotic communication. By considering the properties of amplitude and position modulation, the partial projective synchronization and partial phase synchronization are realized with linear control scheme. The distribution map of optimal synchronization region in the control-parameter space is charted by defining the power consumption of controller. Numerical simulations are executed to confirm the theoretical analysis.
Highlights
Over the past few decades, the dynamics and property of chaotic system have been extensively studied from different points of views as an active topic [1,2,3,4]
The investigation of chaos has benefited the exploration of the complex behavior, intrinsic nonlinear structure of natural system, and the construction of chaotic system, as well as practical applications such as secure communications and signal detection [5,6,7,8,9]
Robust chaotic system can usually provide signal-amplitude modulation by controlling one or some of the parameters in the dynamical equations yet keep the Lyapunov exponents and power spectral density invariable [10,11,12,13,14]. It is a type of chaotic system with potential applications in synchronization, signal processing, image encryption, chaotic radar, and chaotic communication [10, 12]
Summary
Over the past few decades, the dynamics and property of chaotic system have been extensively studied from different points of views as an active topic [1,2,3,4]. Robust chaotic system can usually provide signal-amplitude modulation by controlling one or some of the parameters in the dynamical equations yet keep the Lyapunov exponents and power spectral density invariable [10,11,12,13,14]. It is a type of chaotic system with potential applications in synchronization, signal processing, image encryption, chaotic radar, and chaotic communication [10, 12]. Numerical simulations are shown to further confirm the theoretical analysis
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