Study of a novel conservative chaotic system with special initial offset boosting behaviors

What is it about?

Conservative systems are increasingly being studied, while little research on fractional-order conservative systems has been reported. In this paper, a novel five-dimensional conservative chaotic system is proposed and solved in a fractional-order form using the Adomian decomposition method. This system is dissipative in the phase volume, but the sum of all Lyapunov exponents is zero. During the exploration, some special dynamical behaviors are analyzed in detail by using phase diagrams, bifurcation diagrams, Lyapunov exponential spectra, timing diagrams, and so on. After extensive simulation, several rare dynamical behaviors, including completely homogeneous, homogeneous, and heterogeneous initial offset boosting behaviors, are revealed. Among them, the initial offset boosting behaviors with identical phase trajectory structures have not been reported before, and the previously proposed homogeneous phase trajectories are locally different. By comparing with the integer-order system, two influence factors that affect the system to produce completely homogeneous and heterogeneous conservative flows are discovered. Eventually, the circuit is built on the digital signal processing (DSP) platform to demonstrate the physical realizability of the system. The experimental results are shown by the oscilloscope and agree with the theoretical analysis.

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Photo by Brett Jordan on Unsplash

Photo by Brett Jordan on Unsplash

Why is it important?

The initial offset boosting behavior is one of the particular dynamical behaviors in chaotic systems. According to the structure of different phase trajectories, we can divide them into completely homogeneous, homogeneous, and heterogeneous phase trajectories. The concept of completely homogeneous initial offset boosting behavior is first proposed in this paper. So far, the research on the latter two behavior types is relatively common, but there is no research on the completely homogeneous initial offset boosting behavior. In this paper, a special fractional-order conservative chaotic system is constructed and analyzed. In order to reflect the influence of the order on the system, we also compare the integer-order system with the fractional-order system.

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