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Full-Text Articles in Physical Sciences and Mathematics
Population Dynamics And Bifurcations In Predator-Prey Systems With Allee Effect, Yanni Zeng
Population Dynamics And Bifurcations In Predator-Prey Systems With Allee Effect, Yanni Zeng
Electronic Thesis and Dissertation Repository
This thesis investigates a series of nonlinear predator-prey systems incorporating the Allee effect using differential equations. The main goal is to determine how the Allee effect affects population dynamics. The stability and bifurcations of the systems are studied with a hierarchical parametric analysis, providing insights into the behavioral changes of the population within the systems. In particular, we focus on the study of the number and distribution of limit cycles (oscillating solutions) and the existence of multiple stable states, which cause complex dynamical behaviors. Moreover, including the prey refuge, we examine how our method benefits the low-density animals and affects …
Bifurcation Of Limit Cycles In Smooth And Non-Smooth Dynamical Systems With Normal Form Computation, Yun Tian
Bifurcation Of Limit Cycles In Smooth And Non-Smooth Dynamical Systems With Normal Form Computation, Yun Tian
Electronic Thesis and Dissertation Repository
This thesis contains two parts. In the first part, we investigate bifurcation of limit cycles around a singular point in planar cubic systems and quadratic switching systems. For planar cubic systems, we study cubic perturbations of a quadratic Hamiltonian system and obtain 10 small-amplitude limit cycles bifurcating from an elementary center, for which up to 5th-order Melnikov functions are used. Moreover, we prove the existence of 12 small-amplitude limit cycles around a singular point in a cubic system by computing focus values. For quadratic switching system, we develop a recursive algorithm for computing Lyapunov constants. With this efficient algorithm, we …