Dynamics And Control Of A Class Of Biological Cooperation-competition Systems

In this paper,we concentrate on a generalized two-layer network and its applications in biological cooperation-competition systems.According to the master stability function method and the characteristic spectrum of super-Laplacian matrix,we study the synchronization of the generalized two-layer network,the synchronized behavior and dynamical mechanism of multi-species plant communities.The paper has five chapters,and the main contents are as follows:Chapter 1 mainly introduces the research background,the research status on the synchronization dynamics of multi-layer networks and ecological networks,and the main work of this paper.Chapter 2 provides an overview of the concepts and modeling approaches related to network synchronization dynamics,and proves the relevant conclusion.Chapter 3 investigates the dynamical system for a class of generalized two-layer networks.The master stability equation is derived by variation.According to the maximum Lyapunov exponent of the master stability equation,the synchronization region of the system is determined.And based on the master stability function method,the relationship between the synchronizability of the system and coupling strength is investigated.Finally,the result is verified with numerical simulations and the effect of the number of nodes on the synchronizability of the system is obtained.Chapter 4 studies the synchronization dynamics of plant population in cooperativecompetitive association networks.A two-layer plant association network is constructed by the real plot data,and combined with the logistic model to form the network dynamics system.The synchronization region of this system is determined by the master stability function,and thus the condition for complete synchronization is obtained.Then,the synchronizability of the system is studied through the master stability function method.Finally,the synchronized behavior of plant populations under different coupling strength is analyzed with numerical simulations,and the corresponding ecological mechanism is explained.Chapter 5 summarizes the main work of this paper and looks forward to the future work.