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The effect of seasonal strength and abruptness on predator-prey dynamics. (English) Zbl 1464.92234
There is empirical evidence of a sharp reaction of species to the seasonality of the environment; the shape of the forcing signal cannot be ignored as a simple modeling detail without further investigation of its contribution to population dynamics. Authors evaluate the influence of the sharpness of the seasonal transition on the dynamic behavior of the predator-prey community. Taking into account the potential effect of snow properties on the level of predation, a more or less drastic seasonal effect on the rate of detection of predators is modeled. First follows a brief study of the response to sinusoidal stimulation on detection rate, simulating seasonal changes in a predator’s ability to hunt successfully. Then, the combined effect of the seasonal parameter value and the shape (from sinusoidal to rectangular) of the seasonal impact on the rate of detection of predators is studied, and it is checked whether the arising differences between the impact forms of the signal variance are explained. Thus, since the implementation of sharper seasonal shifts leads the community dynamics to bifurcations and chaotic dynamics due to the lower strength of the seasonal forcing, the form of seasonal forcing stands out as a factor contributing to density fluctuations and the type of observed dynamic behavior.
MSC:
92D25 Population dynamics (general)
92D40 Ecology
34C23 Bifurcation theory for ordinary differential equations
Software:
MATCONT; AUTO
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