Dynamical Characteristics And Synchronization Of Complex-valued Laser Networks

Complex networks exist widely in the real world.The coupling between the nodes of the network can produce interesting dynamical phenomena,such as chaos,bifurcation,multi-stability,amplitude modulation,etc.Network synchronization technology is widely used in secure communication and laser systems.Chaotic synchronization in laser networks is a necessary condition for multi-user communication.Complex-valued laser networks can not only simulate the working mechanism of human brain,but also can access the amplitude and phase information of transmitted signals simultaneously in secure communication,which has strong anti-attack ability.Therefore,the study of the dynamical characteristics and synchronization of complex-valued laser networks has important theoretical significance and application value.This article focuses on complex-valued laser networks with different structures,investigates rich dynamical characteristics,and reveals complex synchronization mechanisms.The main contributions of this article are as follows.Firstly,the dynamical characteristics and synchronization of complex-valued star networks are studied.The dynamical analysis results show that,compared with the periodic states of a complex-valued van der Pol oscillator,chaos,hyper-chaos and multiple coexisting chaotic attractors exist in the star network.The chaotic bifurcation path has strong robustness to the size variation of the star network,and always evolves directly from periodic-1 and quasi-periodic states to chaos,respectively.Complexity versus coupling strength and nonlinear coefficient indicates that the bigger the network size,the larger the parameter range within the chaotic(hyper-chaotic)region.Moreover,the coexistence of chaotic phase synchronization and complete synchronization is found among the peripherals of the star network,which is a symmetry-breaking phenomenon.Secondly,amplitude control and chaotic synchronization of complex-valued laser ring networks are studied.The network exhibits complex dynamics,including hyper-chaos,quasi-period,and coexisting hyper-chaos.Three types of single-parameter oriented amplitude controls are realized with varying or unvarying Lyapunov exponents by a simple control knob in the ring network.Moreover,the mechanism of chaotic synchronization is revealed and chaotic complete synchronization under the strongly coupled state is achieved in the ring network.For the case of weak coupling,quasi-periodic complete synchronization is found.The performance of chaotic synchronization is studied by using the cross-correlation coefficient.The results show that for the same-scale laser network,the improvement and variation trend of synchronization performance are robust to the parity of the number of nodes.Finally,intra-layer synchronization and inter-layer synchronization in complex-valued two-layer networks are studied.Based on Lyapunov stability theory and complex analysis theory,under given significant constraints,the synchronization theorems for intra-layer synchronization and inter-layer synchronization are obtained by using the stability of error systems.The theorems reflect the interaction between network connection topology,coupling modes(intra-layer and inter-layer),and coupling strengths(intra-layer and inter-layer).Based on the complex-valued Lorenz laser system,the theoretical results are further verified and the necessity of constraints is proved by numerical simulations.