Characteristic analysis of a simple fractional-order chaotic system with infinitely many coexisting attractors and Its DSP implementation

Abstract

A new simple third-order chaotic system is proposed. The numerical solution of the proposed chaotic system is calculated by using the Adomian decomposition method. The phenomena of infinitely many coexisting attractors is found in this new chaotic system. This interesting physical phenomenon don’t disappear after fractional-order processing. Conversely, with the order of fractional-order system changes, it shows more complex dynamical characteristic than the original system. In particular, the dynamical behavior of the new fractional-order system is analyzed by using the methods of bifurcation diagram, complexity. Finally, the chaotic attractors are physically implemented by DSP experiment. An extremely simple chaotic system as the demonstration of the fractional-order characteristic, it is of great significance to the application of the special chaotic system in related fields.

Complexity Analysis of Three-Dimensional Fractional-Order Chaotic System Based on Entropy Theory

“…Comparison formula (9) and formula (11), we can clearly see that the fractional-order b chaotic system has only one more nonlinear term compared with the fractional-order a chaotic system, and other structures are the same. Therefore, these two chaotic systems are chosen for convenience of comparison to explore the influence of nonlinear term on the complexity of fractional-order chaotic system.…”

“…Based on the study of integer-order chaotic system, the fractional differential operator is introduced into the system. It is found that when the order is fractional, the system still shows complex chaotic behavior [8][9][10]. Because of its rich dynamic characteristics and potential application value, the research on its dynamic characteristics and application has attracted extensive attention [11][12][13].…”

Solutions and memory effect of fractional-order chaotic system: A review

“…For instance, Wang et al [57] realized the fractionalorder simplified Lorenz system based on the Adomian decomposition method using digital signal processor (DSP). Meanwhile, DSP implementation of fractional-order chaotic system with hidden attractor [154] with infinitely many coexisting attractors, [155,156] with nonhyperbolic equilibrium [157] are carried out. FPGA implementation of fractional-order chaotic systems provides another way which is far more effective due to the parallel arithmetic, such as fractional-order financial chaotic system, [158] fractional-order neuron, [159] fractional-order chaotic oscillators, [138] variable-order fractional chaotic system, [160] fractional-order chaotic sound encryption system.…”

Design and FPGA implementation of a memristor-based multi-scroll hyperchaotic system

“…At present, there are several methods to implement chaotic systems, which include field programmable gate array (FPGA), [32][33][34] analog circuits [35][36][37] and digital signal processing (DSP). [38,39] The analog circuits have some practical difficulties such as sensitivity of components to the temperature, and the aging of the equipments. As the digital signal processors with highprecision operation, the use of FPGA and DSP digital implementations can effectively avoid these problems.…”