Abstract
In this paper, a hyperchaotic circuit consisting of a series memristor, meminductor, and memcapacitor is proposed. The dimensionless mathematical model of the system is established by the state equation of the circuit. The stability of equilibrium point of the system is analyzed by using the traditional dynamic analysis method. Then, the dynamical characteristics of the chaotic system with parameters are analyzed in detail. In addition, the system also has some particular phenomena such as attractor coexistence and state transition. Finally, the circuit is realized by DSP, and the result is consistent with that of numerical simulation. This proves the accuracy of the theoretical analysis. Numerical simulation result shows which hyperchaotic system has very abundant dynamical characteristics.
Highlights
No serial circuit of meminductor, memcapacitor, and memristor has been reported
A chaotic oscillator composed of memcapacitor, meminductor, and memristor in series is presented in this paper. e advantages of the system are that, different from general chaotic circuits, the dynamic behavior of chaotic circuits will be more abundant due to the basic characteristics of meminductor, memcapacitor, and memristor [59,60,61,62]
The system has the phenomenon of hyperchaos, which is not found in the previous simplest series circuit. e disadvantage of this system is that the phase diagram of chaotic attractor is too simple and no new chaotic attractor is generated
Summary
According to LEs, when parameter d changes, the state of the system changes very frequently and there is the hyperchaos phenomenon It can be seen from the bifurcation diagram that the system produces chaos through inverse period doubling. By analyzing its complexity value, we can understand the state change of the chaotic system. When w0 − 10, − 20, − 30, − 40, − 50, and − 60, the coexistence of the six chaotic attractors in the w-x plane is shown in Figure 16(b), where the blue, red, yellow, purple, green and light blue attractors express the size and position with the initial conditions of (4, 50, 1, 24, − 60), (4, 50, 1, 24,− 50), (4, 50, 1, 24, − 40), (4, 50, 1, 24,− 30), (4, 50, 1, 24, − 20), and (4, 50, 1, 24, − 10), respectively
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