The dynamics of the multi-interactions ecological systems

The objective of this book is to study the dynamical behavior of four species syn-ecological models. Two types of four species mathematical model involving different types of ecological interactions is proposed and analyzed. In the first model Holling type –II functional response is a doubted to describe the behavior of predation, while in the second model Lotka-Volterra functional response is used to describe the predation process of the general predator. For the both the models, the existence, uniqueness and boundedness of the solution are discussed. The existences and the stability analysis of all possible equilibrium points are studied. Suitable Lyapunov functions are used to study the global dynamics of the proposed models. Numerical simulations are also carried out to investigate the influence of parameters on the dynamical behavior of the models and to support the obtained analytical results of the both the models.