Grid multi-scroll attractors in cellular neural network with a new activation function and pulse current stimulation

Cellular neural networks (CNNs) have attracted much attention in academia and industry due to their rich dynamic characteristics and potential application value. A tri-cell CNN with a nested sinusoidal activation function (NASF) under a multi-level pulse current stimulation is developed here. The basic features of the CNN system are analyzed from the perspectives of symmetry, dissipativity, and stability of equilibrium points. The complicated dynamical behaviors are thoroughly investigated via phase portraits, Poincaré maps, time series, bifurcation diagrams, Lyapunov exponents, and basins of attraction. It is found that the tri-cell CNN can generate various complex grid multi-scroll attractors (GMSAs). The number of scrolls in GMSAs can be controlled by the logic level of the pulse current and the saturation value of the NSAF. Furthermore, this CNN model can demonstrate intricate initial offset boosting dynamics under the appropriate parameters. This may result in an infinite number of self-excited chaotic attractors and hidden period-1 attractors with identical shapes but different positions, leading to the intriguing coexistence of homogeneous and heterogeneous multistability. The existence of GMSAs with different number of scrolls is verified by MCU-based hardware experiments. Finally, a pseudo-random number generator (PRNG) based on GMSA is designed to explore its potential applications in the field of information security.