https://doi.org/10.1140/epjp/s13360-021-01384-1
Regular Article
Pattern formation in an explosive food chain model: the case of “apparent” mutualism
1
Department of Mathematics & SRM Research Institute, SRM Institute of Science and Technology, 603 203, Kattankulathur, Tamil Nadu, India
2
Department of Mathematics, lowa State University, 50011, Ames, IA, USA
3
Department of Mathematics, University of Georgia, 30602, Athens, GA, USA
4
Department of Mathematics & Computing, Indian Institute of Technology (ISM), 826 004, Dhanbad, Jharkhand, India
Received:
14
November
2020
Accepted:
30
March
2021
Published online:
26
April
2021
In this paper, we have proposed a model system of two preys that mutually contribute to each other with restricted growth rates upon arrival of a generalist predator (who can sexually reproduce) whose predation is followed by Holling type II functional response where three species are self-diffusing for their best of the survival. In spatial case, we investigate the conditions of the blow-up phenomena of sexually reproductive predator of generalist category at finite time. The stability of the system is studied, and we discuss about the conditions of Turing instability. Near bifurcation threshold, major slow down in the dynamical system has been noticed. Variation in the dynamical behaviour of the model system makes structural changes which suggests emergence of patterns. Lastly via numerical simulation, we illustrate different significant patterns such as spots, spots-stripes and stripes which are generated by variation of diffusion parameters and investigate the transition from chaotic to stability properties of the system. Finally, we explain our obtained results where prey exhibits mutual relation among themselves and investigate the populations of the alien/invasive species being fulminated in the ecosystem.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021