On the Solvability of Second-Order Impulsive Differential Equations with Antiperiodic Boundary Value Conditions

We prove existence results for second-order impulsive differential equations with antiperiodic boundary value conditions in the presence of classical fixed point theorems. We also obtain the expression of Green's function of related linear operator in the space of piecewise continuous functions

Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting

The bifurcation properties of a predator prey system with refuge and constant harvesting are investigated. The number of the equilibria and the properties of the system will change due to refuge and harvesting, which leads to the occurrence of several kinds bifurcation phenomena, for example, the saddle-node bifurcation, Bogdanov-Takens bifurcation, Hopf bifurcation, backward bifurcation, separatrix connecting a saddle-node and a saddle bifurcation and heteroclinic bifurcation, and so forth. Our main results reveal much richer dynamics of the system compared to the system with no refuge and harvesting

Antiperiodic Boundary Value Problem for Second-Order Impulsive Differential Equations on Time Scales

We prove the existence results for second-order impulsive differential equations on time scales with antiperiodic boundary value conditions in the presence of classical fixed point theorems

Dynamical behaviors of a two-competitive metapopulation system with impulsive control

Abstract In this paper, we study the dynamical behaviors of a two-competitive metapopulation system with impulsive control and focus on the stable coexistence of the superior and inferior species. A Poincaré map is introduced to prove the existence of a periodic solution and its stability. It is also shown that a stably positive periodic solution bifurcates from the semi-trivial periodic solution through a transcritical bifurcation

Spatio-temporal dynamics of a reaction-diffusion system for a predator-prey model with hyperbolic mortality

We investigate the effects of diffusion on the spatial dynamics of a predator-prey model with hyperbolic mortality in predator population. More precisely, we aim to study the formation of some elementary two-dimensional patterns such as hexagonal spots and stripe patterns. Based on the linear stability analysis, we first identify the region of parameters in which Turing instability occurs. When control parameter is in the Turing space, we analyse the existence of stable patterns for the excited model by the amplitude equations. Then, for control parameter away from the Turing space, we numerically investigate the initial value-controlled patterns. Our results will enrich the pattern dynamics in predator-prey models and provide a deep insight into the dynamics of predator-prey interactions

Spatio-temporal patterns in a predator-prey model with hyperbolic mortality

We investigate the effects of diffusion on the spatial dynamics of a predator-prey model with hyperbolic mortality in predator population. More precisely, we aim to study the formation of some elementary two-dimensional patterns such as hexagonal spots and stripe patterns. Based on the linear stability analysis, we first identify the region of parameters in which Turing instability occurs. When control parameter is in the Turing space, we analyse the existence of stable patterns for the excited model by the amplitude equations. Then, for control parameter away from the Turing space, we numerically investigate the initial valuecontrolled patterns. Our results will enrich the pattern dynamics in predator-prey models and provide a deep insight into the dynamics of predator-prey interactions