Analysis and FPGA implementation of memristor chaotic system with extreme multistability

Abstract

<sec>The memristor is a kind of nonlinear element with nanometer size, which can enhance the complexity of a chaotic system. With the further research of chaos, several novel nonlinear phenomena have been found by scholars, such as hidden attractors, coexisting attractors and multi-stability. Meanwhile, the extremely multi-stability representation system coexists with the infinite attractors, which has become a hot spot in the field of memristor chaos research in recent years. A general method to construct a chaotic systems of multiple coexistence is to increase the number of equilibrium points of chaotic system by means of control. The introduction of memristor results in the linear distribution of the equilibrium points of chaotic system in space, which are the linear equilibrium points. The existing researches show that chaotic system with extremely multi-stability can produce better chaotic sequence, which can be used in engineering fields such as secure communication. Therefore, it is of great significance to construct chaotic systems with rich dynamic behaviors by using memristors.</sec><sec>In order to further improve the complexity of the chaotic system, a five-dimensional memristor chaotic system is constructed by replacing the coupling parameters in the four-dimensional chaotic system based on Sprott-B with a magnetically controlled memristor. The dynamic behavior of the system is analyzed by bifurcation diagram, Lyapunov exponent spectrum, phase portrait, Poincaré map, dynamic map and other conventional means. The analysis shows that the new system has rich dynamic behaviors: when the system parameters change, the system can produce a large number of chaotic attractors with different topological structures and periodic limit cycles with different periods. When different parameters change, the dynamic characteristics of the system also change; when the system parameters are fixed, the system not only has an offset enhancement phenomenon that depends on the change of the initial conditions, but also shows a very strong sensitivity to the initial values and a great adjustment range of the initial values, which leads the infinite chaos and periodic attractors to coexist, namely extremely multi-stability appears. Finally, the digital circuit of the memristor chaotic system is implemented based on the field programmable gate array (FPGA) technology. The phase portrait captured on the oscilloscope is consistent with that from the numerical simulation, which verifies the correctness and realizability of the memristor system.</sec>