Index and impulse in Singular Biological Continuous Systems

A general singular bio-model based on prey-predator variables is proposed in this article. The conditions of bifurcation points caused by singularities were presented. Index and impulse in singular nonlinear systems are represented in the following concepts. The index value and its impulse response will be mentioned for a singular system with three prey-predator and one singular variable. Moreover, It will be shown how SIB points contribute to system complexity, which can be calculated using the index criterion. Finally, simulations and findings related to the topic will be discussed.