95 research outputs found
Estabilidad de un modelo depredador-presa tipo Leslie Gower con un efecto Allee fuerte con retardo
In this paper, a modified Leslie-Gower type predator-prey model introducing in prey population growth a delayed strong Allee effect is studied.
Estabilidad de un modelo depredador-presa tipo Leslie Gower con un efecto Allee fuerte con retardo
The Leslie-Gower model with Allee effect has none, one or two positive equilibrium points but the incorporation of a time delay in the growth rate destabilizes the system, breaking the stability when the delay cross a critical point. The existence of a Hopf bifurcation is studied in detail and the numerical simulations confirm the theoretical results showing the different scenarios. We present biological interpretations for species prey-predator type.En este trabajo se estudia un modelo depredador-presa del tipo Leslie-Gower modificado que introduce en el crecimiento de la población de presas un fuerte efecto Allee retardado.El modelo Leslie-Gower con efecto Allee no tiene ninguno, uno o dos puntos de equilibrio positivos, pero la incorporación de un retardo temporal en la tasa de crecimiento desestabiliza el sistema, rompiendo la estabilidad cuando el retardo cruza un punto crítico. Se estudia en detalle la existencia de una bifurcación de Hopf y las simulaciones numéricas confirman los resultados teóricos mostrando los diferentes escenarios. Presentamos interpretaciones biológicas para especies de tipo presa-predado
Analytical detection of stationary and dynamic patterns in a prey-predator model with reproductive Allee effect in prey growth
Allee effect in population dynamics has a major impact in suppressing the
paradox of enrichment through global bifurcation, and it can generate highly
complex dynamics. The influence of the reproductive Allee effect, incorporated
in the prey's growth rate of a prey-predator model with Beddington-DeAngelis
functional response, is investigated here. Preliminary local and global
bifurcations are identified of the temporal model. Existence and non-existence
of heterogeneous steady-state solutions of the spatio-temporal system are
established for suitable ranges of parameter values. The spatio-temporal model
satisfies Turing instability conditions, but numerical investigation reveals
that the heterogeneous patterns corresponding to unstable Turing eigen modes
acts as a transitory pattern. Inclusion of the reproductive Allee effect in the
prey population has a destabilising effect on the coexistence equilibrium. For
a range of parameter values, various branches of stationary solutions including
mode-dependent Turing solutions and localized pattern solutions are identified
using numerical bifurcation technique. The model is also capable to produce
some complex dynamic patterns such as travelling wave, moving pulse solution,
and spatio-temporal chaos for certain range of parameters and diffusivity along
with appropriate choice of initial conditions Judicious choices of
parametrization for the Beddington-DeAngelis functional response help us to
infer about the resulting patterns for similar prey-predator models with
Holling type-II functional response and ratio-dependent functional response
Multiple Bifurcations and Chaos in a Discrete Prey-Predator System with Generalized Holling III Functional Response
A prey-predator system with the strong Allee effect and generalized Holling type III functional response is presented and discretized. It is shown that the combined influences of Allee effect and step size have an important effect on the dynamics of the system. The existences of Flip and Neimark-Sacker bifurcations and strange attractors and chaotic bands are investigated by using the center manifold theorem and bifurcation theory and some numerical methods
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