Spatiotemporal Chaos in a Sine Map Lattice With Discrete Memristor Coupling
Shaobo He, Bo Yan, Xianming Wu, Huihai Wang, Mengjiao Wang, Herbert Ho‐Ching Iu
Abstract
At present, design of discrete memristor based chaotic maps starts to attract the attention of the scientists, but it is still in its incipient stage. In this paper, spatiotemporal chaos in the Sine map lattice with discrete memristor coupling is investigated. Firstly, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3\times m$ </tex-math></inline-formula> higher dimensional chaotic map is proposed, where there are <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> discrete memristors and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> state variable difference items as the inputs of the discrete memristors. Since it is a spatiotemporal chaotic system, thus it can generate massive chaotic sequences according to the system dimension. Secondly, dynamical characteristics of the system is carried out theoretically and numerically. It shows that there are <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> positive Lyapunov exponents with high complexity. The two examples with one memristor and two memristors are analyzed, and it indicates that the system has rich dynamics including hyperchaos and multistability. Finally, analogue circuit and DSP digital circuit of the two illustrative examples and an Knowm memristor based example are designed to verify the physical realizability of the proposed discrete memristor chaotic maps.