Global dynamics in the leslie-gower model with the allee effect

We complete the global bifurcation analysis of the Leslie-Gower system with the Allee effect which models the dynamics of the populations of predators and their prey in a given ecological or biomedical system. In particular, studying global bifurcations of limit cycles, we prove that such a system can have at most two limit cycles surrounding...

The Termination Principle of Multiple Limit Cycles for the Kukles Cubic System

We carry out the global bifurcation analysis of the Kukles system representing a planar polynomial dynamical system with arbitrary linear and cubic right-hand sides and having an anti-saddle at the origin. Using the <br/>Wintner–Perko termination principle of multiple limit cycles, we solve the problem on the maximum number and distribution of...