The population control of the Lotka-Volterra model is one of the most important and widely investigated issues in mathematical ecology. In this study, assuming that birth rate is controllable and using the Z-type dynamic method, we develop Z-type control laws to drive the prey population and/or predator population to a desired state to keep species away from extinction and to improve ecosystem ...

For three-dimensional competitive Lotka-Volterra systems, Zeeman (1993) identified 33 stable equivalence classes. In this paper we show that: in the case of a heteroclinic cycle on the boundary of the carrying simplex of three-dimensional competitive Lotka-Volterra systems (class 27 in Zeeman’s classification), the conditions (a) there is a pair of purely imaginary eigenvalues at an interior eq...

‎ in this paper, we investigate stability analysis of fractional differential systems equipped with the conformable fractional derivatives. some stability conditions of fractional differential systems are proposed by applying the fractional exponential function and the fractional laplace transform. moreover, we check the stability of conformable fractional lotka-volterra system with the multi-st...

In this work the Homotopy Perturbation Method (HPM) is used to find an exact or approximate solutions of Lotka-Volterra models. Then we compare HPM solution with given by SBA (Somé Blaise Abbo) method.

This article begins with a full description of the quadratic planar vector fields which display two centers. We follow method proposed by Chengzhi Li and provide more detailed analysis different types double centers using classification: Hamiltonian, reversible, Lotka-Volterra, Q4, currently used for fields. also describe completely possible phase portraits their Poincaré compactification. show...