Chaos in periodically forced Holling type IV predator–prey system with impulsive perturbations |
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| Institution: | 1. VKR Centre for Ocean Life, National Institute of Aquatic Resources, Technical University of Denmark, Charlottenlund Slot, Jægersborg Allé, Charlottenlund DK-2920, Denmark;2. Agricultural and Ecological Research Unit, Indian Statistical Institute, Kolkata, West Bengal 700108, India;1. Departamento de Matemáticas, Facultad de Ciencias, UNAM., C. Universitaria, D.F. 04510, México;2. Grupo de Investigación en Sistemas Dinámicos y Aplicaciones (GISDA), Departamento de Matemática, Facultad de Ciencias, Universidad de Bío-Bío, Casilla 5–C, Concepción, VIII–región, Chile |
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| Abstract: | The effect of periodic forcing and impulsive perturbations on predator–prey model with Holling type IV functional response is investigated. The periodic forcing is affected by assuming a periodic variation in the intrinsic growth rate of the prey. The impulsive perturbations are affected by introducing periodic constant impulsive immigration of predator. The dynamical behavior of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that periodic forcing and impulsive perturbation can easily give rise to complex dynamics, including (1) quasi-periodic oscillating, (2) period doubling cascade, (3) chaos, (4) period halfing cascade. |
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