Combinatorics

Attractor

Topology (electrical circuits)

Mathematics

Chebyshev polynomials

Memristor

Engineering

Mathematical analysis

Artificial intelligence

Chebyshev filter

Control (management)

Chaotic

Electronic engineering

Computer science

Applied mathematics

Control theory (sociology)

International Journal of Bifurcation and Chaos

The model of the consecutive memcapacitor has been widely used in chaotic circuits. However, the model of discrete memcapacitor and its application in chaotic systems have not been further studied. In this paper, a model of discrete memcapacitor is proposed. And the dynamical characteristics of the discrete memcapacitor model are analyzed. The memristive Chebyshev map is obtained by coupling the discrete memcapacitor with the Chebyshev map. Since memristive Chebyshev map has linear fixed points, the memristive Chebyshev map is unstable or critically stable, depending on the internal parameters and the initial condition of the chaotic map. The dynamical behavior of control parameter dependence of memristive Chebyshev map is studied by using several analysis methods, and its hyperchaotic attractor is found. The special phenomenon of coexistence of attractors is also found. Finally, the memristive Chebyshev map is realized by DSP. And the results of simulation are further verified. The results of this study supply a theoretical basis for the application of discrete memcapacitor in the design of discrete chaotic systems.

Memcapacitor-Coupled Chebyshev Hyperchaotic Map