Research On Patterns And Complex Dynamics Of Discrete Predator-prey System Based On Coupled Network

Spatiotemporal dynamics and pattern self-organization of predator-prey systems are important research directions of population dynamics.This paper establishes the coupling dynamic network of predator-prey system,based on a variety of neighborhood structures describing different ways of population diffusion.By applying the method of stability analysis,bifurcation analysis,Turing instability analysis,we study the lechanism of pattern self-organization of discrete predator-prey system and explore the complex dynamic behaviors of system,the research reveals spatiotemporal self-organizing structure on the basis of various types of population dispersion.The iollowing results are stated:(1)For Leslie-Gower discrete predator-prey system,the research adopts Moore neighborhood structure to describe the diffusion of the predator and prey populations.constructs the coupled dynamic network model.Based on the linear stability and Turing instability analysis,the pattern formation conditions of the predator-prey system are determined.When conditions are satisfied,the discrete predator-prey system presents complicated types of spatial patterns,including regular gap pattern,stripe pattern,labyrinth patterns,circle patterns,spiral pattern,etc.,and show two new types of stripe-spot and labyrinth pattern with time oscillation and chaotic characteristics.The above patterns are caused by the spatiotemporal symmetry-breaking and show chaotic characteristics.In particular,spiral patterns exhibit that the spatial order is generated by time disorder.These results indicate that the predator-prey system based on the Moore neighborhood structure has more abundant spatiotemporal chaotic patterns than the original system.(2)Through use a variety of typical neighborhood structure to describe different diffusion modes of population,this research investigates pattern dynamics of the Leslie-Gowe discrete predator-prey system based on the coupling network.Seven typical adjacent structures can be divided into types of asymmetrical,axisymmetric and centrosymmetric.When the way of population diffusion is based on asymmetric type adjacent structure,the predator-prey system present self-organization of banded pattern,stripe pattern,curls pattern,spiral pattrrn,etc.;When the way of population diffusion is based on the axisymmetric neighborhood structure,the predator-prey system will also present the mosaic pattern,disordered multistate interlaced pattern;when the way of population diffusion adopts central symmetric neighborhood structure,the predator-prey system shows more abundant spatial pattern types.The above results indicate that the difference for the way of population diffusion greatly affects the spatiotemporal complexity of the predator-prey system.(3)According to the interaction between predator-prey systems,the specific network structure are introduced and applied to coupling Leslie-Gower discrete predator-prey systems.Compared with single predator-prey system,the results of line diagram show that the coupling dynamic network has more abundant nonlinear dynamic behavior.In terms of similarity,the phenomenon of penod-doubling cascades in orbits of period-2,4,8 are showed in the flip bifurcation;in terms of differences,the coupled dynamic network enters the bifurcation and chaos state in advance,expands the chaos region,and presents dynamics behaviors of invariant circles,chaotic sets,periodic window,tori,periodic orbits,and chaotic.This paper studies in two aspects.Firstly,we adopte different ways of population diffusion to explore the spatial pattern formation mechanism of the discrete predator-prey system in view of the system.And the effects of the way of different diffusion on spatial self-organization structure of predator-prey system are demonstrated.Seconed,aceording to interaction between the systems,multiple predator-prey systems are connected on the basis of the specific coupled network structure.And the mechanism of bifurcation and complex dynamic transition from non-chaotic state to chaotic state are studied.These studies on bifurcation and pattern dynamics of predator-prey systems fully demonstrate the complexity of spatiotemporal dynamics of coupled dynamic networks and provide a new perspective for studying the application of coupled networks in predator dynamics.