Abstract
Abstract A model for predator-prey interactions with herd behaviour is proposed. Novelty includes a smooth transition from individual behaviour (low number of prey) to herd behaviour (large number of prey). The model is analysed using standard stability and bifurcations techniques. We prove that the system undergoes a Hopf bifurcation as we vary the parameter that represents the efficiency of predators (dependent on the predation rate, for instance), giving rise to sustained oscillations in the system. The proposed model appears to possess more realistic features than the previous approaches while being also relatively easier to analyse and understand.
Highlights
In the study of ecological interactions in the framework of population dynamics, interactions of the LotkaVolterra type [13] are a useful simplification
We prove that the system undergoes a Hopf bifurcation as we vary the parameter that represents the efficiency of predators, giving rise to sustained oscillations in the system
A. de Assis et al Applied Mathematics and Nonlinear Sciences 5(2020) 11–24 studied the data and hypotheses regulating the interactions between species, focusing on the predator-prey case, and proposed several types of “response functions” [6]
Summary
A. Instituto de Ciências Naturais Humanas e Sociais, Universidade Federal de Mato Grosso, Av. Alexandre Ferronato 1200, Setor Industrial, 78557267 Sinop, MT, Brazil. C. Dipartimento di Matematica “Giuseppe Peano”, Università di Torino,via Carlo Alberto 10, 10123 Torino, Italy. Member of the INdAM research group GNCS. Received March 9th 2019 Accepted September 23rd 2019 Available online January 31st 2020
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