2 research outputs found
Editorial: Recent advances in bifurcation analysis: theory, methods, applications and beyond - volume II
Multiple wave solutions in a diffusive predator-prey model with strong Allee effect on prey and ratio-dependent functional response
A thorough analysis is performed in a predator-prey reaction-diffusion model
which includes three relevant complex dynamical ingredients: (a) a strong Allee
effect; (b) ratio-dependent functional responses; and (c) transport attributes
given by a diffusion process. As is well-known in the specialized literature,
these aspects capture adverse survival conditions for the prey, predation
search features and non-homogeneous spatial dynamical distribution of both
populations. We look for traveling-wave solutions and provide rigorous results
coming from a standard local analysis, numerical bifurcation analysis, and
relevant computations of invariant manifolds to exhibit homoclinic and
heteroclinic connections and periodic orbits in the associated dynamical system
in . In so doing, we present and describe a diverse zoo of traveling wave
solutions; and we relate their occurrence to the Allee effect, the spreading
rates and propagation speed. In addition, homoclinic chaos is manifested via
both saddle-focus and focus-focus bifurcations as well as a Belyakov point. An
actual computation of global invariant manifolds near a focus-focus homoclinic
bifurcation is also presented to enravel a multiplicity of wave solutions in
the model. A deep understanding of such ecological dynamics is therefore
highlighted.Comment: 35 pages, 22 figure