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Mathematical Methods in the Applied Sciences, Volume 48, Issue 2, Page 2194-2223, 30 January 2025.The impact of predator‐driven fear on ecosystems is significant and can encompass both trophic (direct) and nontrophic (indirect) effects. Previous studies have shown that nontrophic fear effects have an important role in predator–prey dynamics. This study investigates the nontrophic fear effect on prey caused by generalist predators and explores ...
Anuj Kumar Umrao +2 more
wiley +1 more source
Bifurcations of cubic homoclinic tangencies in two-dimensional symplectic maps
, 2017 We study bifurcations of cubic homoclinic tangencies in two-dimensional symplectic maps. We distinguish two types of cubic homoclinic tangencies, and each type gives different first return maps derived to diverse conservative cubic H\'enon maps with ...
Gonchenko, Marina +2 more
core +1 more source
Bifurcations of planar sliding homoclinics [PDF]
Mathematical Problems in Engineering, 2006 We study bifurcations from sliding homoclinic solutions to bounded solutions on ℝ for certain discontinuous planar systems under periodic perturbations. Sufficient conditions are derived for such perturbation problems.
Michal Fečkan +2 more
openaire +2 more sources
Population dynamics in a Leslie–Gower predator–prey model with predator harvesting at high densities
Mathematical Methods in the Applied Sciences, Volume 48, Issue 1, Page 804-838, 15 January 2025.In this paper, we propose a Leslie–Gower predator–prey model in which the predator can only be captured when its population size exceeds a critical value; the mean growth rate of the prey in the absence of the predator is subject to a semi‐saturation rate that affects its birth curve, and the interaction between the two species is defined by a Holling ...
Christian Cortés García
wiley +1 more source
Delay-induced multistability near a global bifurcation
, 2007 We study the effect of a time-delayed feedback within a generic model for a saddle-node bifurcation on a limit cycle. Without delay the only attractor below this global bifurcation is a stable node.
E. SCHÖLL +5 more
core +1 more source
Bifurcation diagrams for singularly perturbed system
Electronic Journal of Qualitative Theory of Differential Equations, 2012 We consider a singularly perturbed system where the fast dynamic of the unperturbed problem exhibits a trajectory homoclinic to a critical point.
Matteo Franca
doaj +1 more source
IET Generation, Transmission &Distribution, Volume 19, Issue 1, January/December 2025.1. The reactive current injection system has infinite saddle points, and for every saddle point, there are two special lines (the blue lines in Figure 2). When the initial states are situated on the special lines, the final states of the reactive current injection will converge to the saddle points. 2.
Shuaishuai Lv +7 more
wiley +1 more source
Noisy homoclinic pulse dynamics [PDF]
, 2016 The effect of stochastic perturbations on nearly homoclinic pulse trains is considered for three model systems: a Duffing oscillator, the Lorenz-like Shimizu–Morioka model, and a co-dimension-three normal form.
Balmforth, Neil J., Eaves, Tom
core +2 more sources
Journal of Mathematics, Volume 2025, Issue 1, 2025.This research describes a predator–prey system that takes into account the generalized Allee effect, aiming to derive general conclusions applicable to specific Allee effect functions through the use of a generalized function. To make sure the suggested model was accurate from a mathematical perspective, we first investigated the solutions to determine
Gaji Zhuo +5 more
wiley +1 more source
Multistable Solitons in the Cubic-Quintic Discrete Nonlinear Schr\"odinger Equation
, 2005 We analyze the existence and stability of localized solutions in the one-dimensional discrete nonlinear Schr\"{o}dinger (DNLS) equation with a combination of competing self-focusing cubic and defocusing quintic onsite nonlinearities.
Alfimov +53 more
core +1 more source