title: Wave of chaos in a spatial eco-epidemiological system: Generating realistic patterns of patchiness in rabbit-lynx dynamics.
abstract: In the present paper, we propose and analyze an eco-epidemiological model with diffusion to study the dynamics of rabbit populations which are consumed by lynx populations. Existence, boundedness, stability and bifurcation analyses of solutions for the proposed rabbit-lynx model are performed. Results show that in the presence of diffusion the model has the potential of exhibiting Turing instability. Numerical results (finite difference and finite element methods) reveal the existence of the wave of chaos and this appears to be a dominant mode of disease dispersal. We also show the mechanism of spatiotemporal pattern formation resulting from the Hopf bifurcation analysis, which can be a potential candidate for understanding the complex spatiotemporal dynamics of eco-epidemiological systems. Implications of the asymptotic transmission rate on disease eradication among rabbit population which in turn enhances the survival of Iberian lynx are discussed.
authors.affiliation: Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad- 826 004. Jharkhand, INDIA. Electronic address: ranjit_ism@yahoo.com.
authors.forename: Ranjit Kumar
authors.initials: RK
authors.lastname: Upadhyay
authors.affiliation: School of Mathematics, Thapar University, Patiala-147004, Punjab, INDIA.
authors.forename: Parimita
authors.initials: P
authors.lastname: Roy
authors.affiliation: School of Mathematics and Statistics, Mathematical Institute, North Haugh, St Andrews KY16 9SS, Scotland.
authors.forename: C
authors.initials: C
authors.lastname: Venkataraman
authors.affiliation: Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Pev III, 5C15, Brighton BN19QH, United Kingdom.
authors.forename: A
authors.initials: A
authors.lastname: Madzvamuse
mesh_terms: D000818:Animals; D020387:Food Chain; D046008:Lynx; D008954:Models, Biological; D017711:Nonlinear Dynamics; D011817:Rabbits
keywords: Bifurcations analysis; Diffusion-driven instability; Eco-epidemiological model; Turing patterns