A study of chaos and its control in a harvested tri-trophic food chain model with alternative food source and diffusion effect

The present paper explores a tri-trophic food chain model with alternative food source for prey species and harvesting in prey and intermediate predator. We perform the local dynamical analysis of the model system. We also derive conditions for Turing instability in the diffusive model. To investigate the global dynamics we have performed extensive numerical experiments in the both non-diffusive and diffusive system. We find that harvesting has an important role in preventing chaotic dynamics and sustaining the ecosystem. It is noticed that alternative food also has a stabilizing effect on chaotic dynamics and leads a stable dynamics through chaos, period-doubling and limit cycles.Thus both the harvesting parameter and alternative food may be considered as bio-controlling parameters for controlling chaotic dynamics in three species food chain model. In the diffusive system we observed that the harvesting parameter and alternative food may cause Turing instability.