A Fractional-Order Chaotic System With Infinite Attractor Coexistence and its DSP Implementation

Abstract

In this paper, the fractional calculus is introduced into a simplest memristive circuit to construct a new four-dimensional fractional-order chaotic system. Combining conformable differential definition and Adomian decomposition method (ADM) algorithm is used to solve the numerical solution of the system. The attractor coexistence of the fractional-order system is investigated from the attractor phase diagram, coexistence bifurcation model, coexistence Lyapunov exponent spectrum and attractor basin. In addition, the hardware circuit of the system is implemented on the DSP platform. The simulation results show that the fractional-order chaotic system exhibits rich dynamic characteristics. In particular, the initial value of the system could control the offset, amplitude and frequency of the attractor better, and increase the complexity and randomness of the chaotic sequences. The research provides theoretical basis and guidance for the applications of fractional-order chaotic system.

Dynamic analysis of a fractional-order hyperchaotic system and its application in image encryption

“…The maximum error range of each parameter and initial value in the decryption process is obtained by numerical simulation, where q is -10 , 16 a i ( = i 1, 2, 4,...,8), x x , 1 2 are -10 15 and a , 3 x , 3 x 4 are -10 . 14 Therefore, the key space is ´´´» + ´+ 4 8 6 10 2 , 3 8 16 15 9 14 3 672 which is much larger than the theoretical key space value 2 100 [58] of the cryptosystem. In addition, the key space size of the designed scheme is compared with that in the existing literature [22,23,40], and the results are shown in table 3.…”

“…In the encryption process, the closer the digital transmission distance of the encrypted data, the better the encryption performance. Through numerical simulations, histograms of plaintext Sailboat, Fruits and Pepper images in R, G and B channels are obtained, as shown in figure 12 (b3) = +x 2.6 10 , 3 14 (b4) = +x 2.8 10 , 4 14 (b5) = +q 0.74 10 , 16 (b6) = +a 10 10 , 1 14 (b7) = +a 5 10 . Table 3.…”

“…In 1963, Lorenz [2] proposed the concept of chaos theory. Since then, scholars began to study various chaotic models, such as continuous chaotic system [3][4][5], discrete chaotic system [6,7], complex chaotic system [8][9][10], time-delay chaotic system [11,12] and fractional chaotic system [13][14][15]. Due to the unpredictability, ergodicity and extremely sensitivity to initial conditions of chaotic system [16], it is eminently suitable for chaotic cryptography.…”

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

“…The most common methods for solving fractional-order chaotic systems are frequency domain method (FDM) [48,49], predictor-corrector method (PCM) [50,51], and Adomian decomposition method (ADM) [52,53]. As a numerical resolution algorithm, ADM is more accurate than FDM and PCM numerically and theoretically [53].…”

Novel Solution for Time-fractional Klein-Gordon Equation with Different Applications

“…Authors have been focusing on the numerical solutions of FPDEs with these novel fractional derivative operators over the past few years while considering a variety of fractional orders. According to the article (Liu et al, 2020), authors have developed a new four-dimensional fractional-order chaotic system using fractional calculus for the simplest memristive circuit. However, some authors, in the reference (Wang et al, 2022), have analyzed the numerical solution of travelling waves in chemical kinetics.…”