Bifurcations, and temporal and spatial patterns of a modified Lotka-Volterra model

Edward A. McGehee, Noel Schutt, Desiderio A. Vasquez, Enrique Peacock-LÓpez

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

34 Citas (Scopus)

Resumen

Bazykin proposed a Lotka-Volterra-type ecological model that accounts for simplified territoriality, which neither depends on territory size nor on food availability. In this study, we describe the global dynamics of the Bazykin model using analytical and numerical methods. We specifically focus on the effects of mutual predator interference and the prey carrying capacity since the variability of each could have especially dramatic ecological repercussions. The model displays a broad array of complex dynamics in space and time; for instance, we find the coexistence of a limit cycle and a steady state, and bistability of steady states. We also characterize super- and subcritical Poincaré-Andronov-Hopf bifurcations and a Bogdanov-Takens bifurcation. To illustrate the system's ability to naturally shift from stable to unstable dynamics, we construct bursting solutions, which depend on the slow dynamics of the carrying capacity. We also consider the stabilizing effect of the intraspecies interaction parameter, without which the system only shows either a stable steady state or oscillatory solutions with large amplitudes. We argue that this large amplitude behavior is the source of chaotic behavior reported in systems that use the MacArthur-Rosenzweig model to describe food-chain dynamics. Finally, we find the sufficient conditions in parameter space for Turing patterns and obtain the so-called "back-eye" pattern and localized structures.

Idioma originalInglés
Páginas (desde-hasta)2223-2248
Número de páginas26
PublicaciónInternational Journal of Bifurcation and Chaos
Volumen18
N.º8
DOI
EstadoPublicada - ago. 2008
Publicado de forma externa

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