Results 81 to 90 of about 6,100 (243)
Limit Cycles Bifurcated from Some Z4-Equivariant Quintic Near-Hamiltonian Systems
Abstract and Applied Analysis, 2014 We study the number and distribution of limit cycles of some planar Z4-equivariant quintic near-Hamiltonian systems. By the theories of Hopf and heteroclinic bifurcation, it is proved that the perturbed system can have 24 limit cycles with some new ...
Simin Qu +3 more
doaj +1 more source
New approach to study the van der Pol equation for large damping
Electronic Journal of Qualitative Theory of Differential Equations, 2018 We present a new approach to establish the existence of a unique limit cycle for the van der Pol equation in case of large damping. It is connected with the bifurcation of a stable hyperbolic limit cycle from a closed curve composed of two heteroclinic ...
Klaus Schneider
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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
Continuation of connecting orbits in 3D-ODEs: (I) Point-to-cycle connections
, 2007 We propose new methods for the numerical continuation of point-to-cycle connecting orbits in 3-dimensional autonomous ODE's using projection boundary conditions.
Afraimovich V. S. +5 more
core +4 more sources
Bifurcation Diagrams and Heteroclinic Networks of Octagonal H-Planforms [PDF]
Journal of Nonlinear Science, 2012 This paper completes the classification of bifurcation diagrams for H-planforms in the Poincar ́e disc D whose fundamental domain is a regular octagon. An H-planform is a steady solution of a PDE or integro-differential equation in D, which is invariant under the action of a lattice subgroup Γ of U(1,1), the group of isometries of D.
Faye, Grégory, Chossat, Pascal
openaire +3 more sources
Stability of Standing Periodic Waves in the Massive Thirring Model
Studies in Applied Mathematics, Volume 154, Issue 1, January 2025.ABSTRACT We analyze the spectral stability of the standing periodic waves in the massive Thirring model in laboratory coordinates. Since solutions of the linearized MTM equation are related to the squared eigenfunctions of the linear Lax system, the spectral stability of the standing periodic waves can be studied by using their Lax spectrum.
Shikun Cui, Dmitry E. Pelinovsky
wiley +1 more source
Complex Dynamics and Chaos Control of Discrete Prey–Predator Model With Caputo Fractional Derivative
Complexity, Volume 2025, Issue 1, 2025.This work examines a discrete prey–predator model using the fractional derivative. The conditions for the existence and stability of the fixed points in the model are identified. The analysis is centered on exploring various bifurcations at the positive fixed point to understand their ecological implications.
Rowshon Ara +2 more
wiley +1 more source
Nonlinear semelparous Leslie models
Mathematical Biosciences and Engineering, 2005 In this paper we consider the bifurcations that occur at the trivial equilibrium of a general class of nonlinear Leslie matrix models for the dynamics of a structured population in which only the oldest class is reproductive.
J. M. Cushing
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Homoclinic and Heteroclinic Bifurcations in rf SQUIDs
Zeitschrift für Naturforschung A, 1988 Abstract The Melnikov method is used to discuss the parameter dependence of homoclinic and heteroclinic bifurcations for the rf SQUID system. Also the case of strong damping is treated. Because of the complicated potential the resulting integrals have to be evaluated numerically.
B. P. Koch, B. Bruhn
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Ecology, Volume 105, Issue 2, February 2024.Abstract A growing body of literature recognizes that pairwise species interactions are not necessarily an appropriate metaphorical molecule of community ecology. Two examples are intransitive competition and nonlinear higher‐order effects. While these two processes have been discussed extensively, the explicit analysis of how the two of them behave ...
John Vandermeer, Ivette Perfecto
wiley +1 more source