Lotka–Volterra equation

Introduction The Lotka-Volterra equations are used in biology, chemistry, and many other sciences that deal with two populations whether that be in our case animal, or chemical, where two species both rely on a single source to stay alive, called a Competitive model (Appendix A), or where one species relies on another species to stay alive, called a Predator/Prey Model (Appendix B). Initially, the Lotka-Volterra predator-prey model was stated by Alfred K. Lotka. This was a similar equation to the logistic

the competitors predates on one of the other competitors is considered. Quantitative analyses of non-negativity and boundedness of solution trajectories, dissipativity, and behavior around equilibria, global stability and persistence of the model equations are analyzed. We present the global stability of equilibria by constructing a Lyapunov function. Hopf bifurcation theory is applied. Keywords: Chemostat; Food web; Global stability; Hopf bifurcation; Dissipative. 1. Introduction In microbiology