Pattern formation and control of spatiotemporal chaos in a reaction diffusion prey–predator system supplying additional food |
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| Institution: | 1. Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University, Xi’an 710049, China;2. The School of Electronic and Information Engineering, Southwest University, Chongqing 400715, China;3. Key Lab for IOT and Information Fusion Technology of Zhejiang, Hangzhou Dianzi University, Hangzhou 310018, China;1. Department of Computer Science, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA;2. Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA;3. Department of Physics, University of Guilan, P.O. Box 41335-1914, Rasht, Iran;4. Research Institute for Applied Physics and Astronomy, University of Tabriz, Tabriz, Iran;5. Department of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran |
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| Abstract: | Spatiotemporal dynamics of a predator–prey system in presence of spatial diffusion is investigated in presence of additional food exists for predators. Conditions for stability of Hopf as well as Turing patterns in a spatial domain are determined by making use of the linear stability analysis. Impact of additional food is clear from these conditions. Numerical simulation results are presented in order to validate the analytical findings. Finally numerical simulations are carried out around the steady state under zero flux boundary conditions. With the help of numerical simulations, the different types of spatial patterns (including stationary spatial pattern, oscillatory pattern, and spatiotemporal chaos) are identified in this diffusive predator–prey system in presence of additional food, depending on the quantity, quality of the additional food and the spatial domain and other parameters of the model. The key observation is that spatiotemporal chaos can be controlled supplying suitable additional food to predator. These investigations may be useful to understand complex spatiotemporal dynamics of population dynamical models in presence of additional food. |
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