Chaos anti-control of coexisting infinite signals and pinning synchronization of a complex-valued laser chain network

There are many applications of chaos anti-control from its inherent state to the expected chaotic state in different disciplines ranging from engineering to biology and social sciences. This paper studies the dynamical characteristics, chaos anti-control of coexisting attractors, and pinning synchronization of a complex-valued laser chain network (CVLCN). Firstly, a CVLCN based on the complex-valued Lorenz laser systems is developed, and detailed dynamic analyses for the important parameters are executed to obtain significant results of the hyper-chaotic attractors and quasi-periodic attractors, which are confirmed by phase bifurcation diagram, Lyapunov exponent spectrum, the Kaplan-Yorke dimension, and power spectrum. A key point of this paper is the discovery of the coexistence of infinite hyper-chaotic attractors and quasi-periodic attractors. Given the vital role of oscillations and network dynamics in neural processes related to health and disease, the presence of quasi-periodic signals may indicate an irregular brain state. Therefore, a suitable controller is designed to realize intermittent and non-intermittent chaos anti-control of the coexisting infinite quasi-periodic signals. Finally, the pinning controller is designed to achieve the network synchronization by the theoretical and numerical simulation research.