Dynamic Analysis and DSP Implementation of Memristor Chaotic Systems with Multiple Forms of Hidden Attractors

Abstract

In this paper, a new six dimensional memristor chaotic system is designed by combining the chaotic system with a memristor. By analyzing the phase diagram of the chaotic attractors, eleven different attractors are found, including a multi-wing attractor and symmetric attractors. By analyzing the equilibrium point of the system, it is proven that the system has the property of a hidden chaotic attractor. The dynamic behavior of the system when the three parameters change is analyzed by means of LEs and a Bifurcation diagram. Other phenomenon, such as chaos degradation, coexistence of multiple attractors and bias boosting, are also found. Finally, the simulation on the DSP platform also verifies the accuracy of the chaotic system simulation. The theoretical analysis and simulation results show that the system has rich dynamical characteristics; therefore, it is suitable for secure communication and image encryption and other fields.

Multistability Mechanisms for Improving the Performance of a Piezoelectric Energy Harvester with Geometric Nonlinearities

“…In this case, the attractor around O(0, 0) at ˆ0.36 c = is enlarged, and the BA of the higher amplitude attractor around O(0, 0) at ˆ0.37 c = is fur- When f 0 increases to 0.007, bistability around each nontrivial center also appears in system (4) at ĉ = 0.36 and ĉ = 0.37 (see Figure 9(c-1,c-2)). Even though the new attractors are of much higher amplitudes, their BAs are so small and fractal that they are called rare and hidden attractors [32][33][34]. Accordingly, it is almost impossible for system (3) to achieve these attractors.…”

Dynamical analysis and circuit implementation of a memristive chaotic system with infinite coexisting attractors

“…On the other hand, Li et al introduced a memristor into a jerk system and proposed a four-dimensional memristive chaotic system, which exhibits rich dynamical behaviors including extreme multi-stability and offset boosting [17]. Guo et al integrated a memristor with a chaotic system and devised a novel six-dimensional memristive chaotic system, in which they observed phenomena such as chaotic degeneration, coexistence of multiple attractors, and offset boosting [18]. Zeng et al proposed a special memristor-based Jerk system, which found the sensitivity of the initial state of the system and generated complex behaviors such as multi-stablestates [19].…”

“…According to formula(18) and(19), we get thatC 1 = C 2 = C 3 = C 4 = 1 uF, R 11 = R 14 = 10 kΩ, R 7 = 45.5 kΩ, R 6 = 6.25 kΩ, R 10 = 100 Ω, R 8 = 1.428 kΩ, R 15 = 3.33 kΩ, R 26 = 1 MΩ, R 21 = 560 Ω. In the part of the circuit of the tanh, R 1 = R 3 = R 4 =1 kΩ, R 13 = R 16 = R 17 = R 18 = R 12 =10 kΩ, R 2 = 520 Ω, R 5 = 7.2 kΩ, R 9 = 11.646 k.…”

Rucklidge-based memristive chaotic system: Dynamic analysis and image encryption

“…However, it was not until 2008 that HP Labs made a solid-state memristor, [8] which marks that the research on memristors has officially changed from theory to practice. With the deepening of the research on memristors, [9,10] the special nonlinearity and nonvolatility of memristors have made them widely used in chaos, [11][12][13] neural networks, [14][15][16][17][18][19][20] secure communication, [21,22] memory, [23] neurons, [24] and chaotic oscillators. [25,26] More and more researchers have found that adding memristors to chaotic circuits will greatly increase the complexity of the system and cause some other behaviors in the chaotic system.…”