Abstract
As a new type of nonlinear electronic component, a memristor can be used in a chaotic system to increase the complexity of the system. In this paper, a flux-controlled memristor is applied to an existing chaotic system, and a novel five-dimensional chaotic system with high complexity and hidden attractors is proposed. Analyzing the nonlinear characteristics of the system, we can find that the system has new chaotic attractors and many novel quasi-periodic limit cycles; the unique attractor structure of the Poincaré map also reflects the complexity and novelty of the hidden attractor for the system; the system has a very high complexity when measured through spectral entropy. In addition, under different initial conditions, the system exhibits the coexistence of chaotic attractors with different topologies, quasi-periodic limit cycles, and chaotic attractors. At the same time, an interesting transient chaos phenomenon, one kind of novel quasi-periodic, and weak chaotic hidden attractors are found. Finally, we realize the memristor model circuit and the proposed chaotic system use off-the-shelf electronic components. The experimental results of the circuit are consistent with the numerical simulation, which shows that the system is physically achievable and provides a new option for the application of memristive chaotic systems.
Highlights
Since the discovery of the first chaotic attractor by meteorological scientist Lorenz in 1963 [1], scholars have continued to research and explore new chaotic systems composed of ordinary differential equations
Distinguishing from the traditional chaotic system which has one or more unstable saddle focal points, hidden attractors are a new type of attractor that has been proposed in recent years
The hidden attractor is not excited by the unstable equilibrium point, and its attraction basin does not intersect with any unstable equilibrium point, which is the biggest
Summary
Since the discovery of the first chaotic attractor by meteorological scientist Lorenz in 1963 [1], scholars have continued to research and explore new chaotic systems composed of ordinary differential equations. If it is used to couple with the existing chaotic system, it will be more likely to produce chaotic behavior It seems that memristive chaotic systems are more suitable for applications in chaotic encryption and other technologies [41], there is only a few literature on hidden chaotic systems implemented with memristor models [41,42]. Since the equivalent realization circuit for memristor and the memristive system both are implemented with some off-the-shelf components, it is expected that the system will contribute greatly to further research and applications. It is verified that there are infinite attractors and transient periodic dynamics behavior in memristor chaotic systems, depending on the initial conditions. A New 5-D Memristive Chaotic System verified that there areNew infinite attractors and transient
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