Dinamika Model Populasi Spesies Tunggal pada Lingkungan Tercemar dengan Waktu Tunda Tunggal Diskret

Abstract

This manuscript describes a single-species population model in a polluted environment. This model describes the stability of a single-species population behavior which is affected by the pollution effect. The focus of stability is restricted, the stability of behavior when there is no additional of exogenous pollutants into the polluted environment and the opposite condition, there is an additional of exogenous pollutants into the environment. For a certain fixed point, a condition of local stability behavior was determined by Routh-Hurwitz criterion and the behavior of global stability was analyzed by Lyapunov function. Changing the value of parameters system such as the parameter of additional of exogenous pollutants into the polluted environment will trigger Hopf bifurcation existence. The occurrence of Hopf bifurcation was analyzed by Liu criterion that related to the Routh-Hurwitz criterion. A single-species population model in this manuscript also describes the effect of a single discrete time delay as a realization that the absorption of pollutants was not immediately absorbed by the population, but needing a time to contaminate the population. Furthermore, the time delay was estimated by using the Nyquist criterion in order to maintain the stability of the model. Mathematical simulation using a software was used to illustrate the results of models analysis.