Dynamical Characteristics And Complex Synchronization Of Laser Complex Systems

Complex variables widely exist in laser,fluid,electromagnetic field and other physical fields.In recent years,the dynamics of systems with complex variables(referred to as"complex systems"),such as laser detuning,chaotic bifurcation and coexistence of attractors have attracted great attention.Chaotic synchronization of laser complex system is a necessary condition for laser chaotic secure communication.Real variable is a special case when the imaginary part of complex variable is zero.Therefore,the study of dynamics of laser complex system is more complex and difficult than that of real system.In the field of laser chaotic secure communication,complex variables and complex parameters can increase the content and security of information transmission.Therefore,it is of great theoretical and practical significance to study the dynamical characteristics and complex synchronization of laser complex system.In this paper,the chaotic dynamical characteristics of different laser complex chaotic systems(networks)are studied by basic dynamic analysis methods,such as Lyapunov exponent,bifurcation diagram,phase diagram,basin of attraction,SE complexity algorithm and C₀complexity algorithm.At the same time,based on Lyapunov stability theorem and other mathematical theory tools,using the method of theoretical proof and numerical simulation,some synchronization problems are analyzed.The main contents of this paper are as follows.Firstly,the dynamics and complex self synchronization of a laser system with complex variables and parameters are studied.The results of dynamics show that the system not only has period-doubling bifurcation,period-3 bifurcation and axis-symmetric coexisting attractor,but also has the intermittent chaos and infinite transition of period and sink.At the same time,two chaotic attractors with different structures are implemented on DSP.Based on complex laser system,a complex self synchronization scheme is proposed.The synchronization of homogeneous and heterogeneous coexisting attractors in complex domain is numerically simulated.Secondly,the dynamics and complex generalized synchronization of complex chaotic systems with single parameter are studied.A one-parameter complex chaotic system with the same nonlinear term as the complex Lorenz system but simpler linear term is proposed.The system has infinitely many equilibrium points,multistability and extreme multistability.The energy of the system is estimated by Hamiltonian energy function.The definition of complex generalized synchronization is introduced,that is,a complex vector map is designed so that the response system can be asymptotically synchronized to the driving chaotic system.Based on Lyapunov stability theory,the correctness of the complex generalized synchronization scheme is strictly proved.Finally,the complex generalized synchronization of a one-parameter complex chaotic system with coexisting chaotic attractors and two strictly different complex chaotic systems are obtained.Finally,the dynamics and synchronization of the complex-valued ring network are studied.Based on the van der Pol oscillator in the second-order complex domain,a nearest ring network model is designed.It is found that the network has only one bifurcation(or reverse bifurcation)path from period one to chaos(hyperchaos).The periodic state has only period-one attractor.With the increase of the number of nodes in the ring network,the range of coupling parameters of chaos in the network also increases.The complexity of three nodes and four nodes ring network increases with the decrease of coupling parameters.The change of coupling parameters has little effect on the complexity of 25 nodes network.There are periodic phase synchronization and chaotic phase synchronization between different nodes of ring network.