Two-dimensional memristive hyperchaotic maps with different coupling frames and its hardware implementation

Abstract

Continuous-time memristors have been used in numerous chaotic circuit systems. Similarly, the discrete memristor model applied to a discrete map is also worthy of further study. To this end, this paper first proposes a discrete memristor model and analyzes the voltage–current characteristics of the memristor. Also, the discrete memristor is coupled with a one-dimensional (1D) sine chaotic map through different coupling frameworks, and two different two-dimensional (2D) chaotic map models are generated. Due to the presence of linear fixed points, the stability of the 2D memristor-coupled chaotic map depends on the choice of control parameters and initial states. The dynamic behavior of the chaotic map under different coupled map frameworks is investigated by using various analytical methods, and the results show that different coupling frameworks can produce different complex dynamical behaviors for memristor chaotic maps. The dynamic behavior based on parameter control is also investigated. The numerical experimental results show that the change of parameters can not only enrich the dynamic behavior of a chaotic map, but also increase the complexity of the memristor-coupled sine map. In addition, a simple encryption algorithm is designed based on the memristor chaotic map under the new coupling framework, and the performance analysis shows that the algorithm has a strong ability of image encryption. Finally, the numerical results are verified by hardware experiments.

Applying exponential unit for breaking symmetry of memristive maps

“…Discrete maps and chaotic maps are fundamental concepts in the realm of dynamical systems and nonlinear dynamics, with applications spanning various scientific disciplines and engineering fields [23][24][25][26]. Chaotic maps, in particular, are characterized by their sensitivity to initial conditions, leading to seemingly random and unpredictable behavior that conceals underlying patterns [27,28]. These maps find applications in cryptography, secure communications, random number generation, and even in modeling complex natural phenomena.…”

“…This innovative approach opens up new possibilities for designing more robust cryptographic systems, further extending the practical applications of chaotic maps in the digital age [31][32][33]. Memristive maps with hyperchaos were introduced in [18,27]. Liu et al [29] used sine memristance to improve discrete maps.…”

Design of High-Dimensional Maps with Sine Terms

“…Furthermore, memristors could be used in artificial intelligence, neuromorphic computing, and analog signal processing [12][13][14]. This has led to significant interest in the memristor from both the academic and industrial communities, with many researchers working to explore its full potential [15,16] Memristors have been shown to be capable of generating chaotic behavior, and this property can be exploited to create new discrete chaotic maps [17][18][19][20][21]. Generally, authors explore 2D memristive maps due to their simplicity.…”

Coexisting Firing Patterns in an Improved Memristive Hindmarsh–Rose Neuron Model with Multi-Frequency Alternating Current Injection

“…Furthermore, with the continuous development of memristor theory, the application of memristor in many fields has achieved remarkable results and has bright development prospects [10][11][12][13][14]. It has developed rapidly in the fields of memristor neurons and neural network dynamics.…”