Results 51 to 60 of about 3,877 (218)
Chaos in Coupled Heteroclinic Cycles and its Piecewise-Constant Representation [PDF]
, 2022 Arkady Pikovsky, Alexander Nepomnyashchy
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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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Heteroclinic Dynamics of Localized Frequency Synchrony: Heteroclinic Cycles for Small Populations [PDF]
Journal of Nonlinear Science, 2019 Many real-world systems can be modeled as networks of interacting oscillatory units. Collective dynamics that are of functional relevance for the oscillator network, such as switching between metastable states, arise through the interplay of network structure and interaction.
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Abstract and Applied Analysis, 2013 A delayed Leslie-Gower predator-prey model with nonmonotonic functional response is studied. The existence and local stability of the positive equilibrium of the system with or without delay are completely determined in the parameter plane.
Jiao Jiang, Yongli Song
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, 2018 Using a vector field in $\mathbb{R}^4$, we provide an example of a robust heteroclinic cycle between two equilibria that displays a mix of features exhibited by well-known types of low-dimensional heteroclinic structures, including simple, quasi-simple and pseudo-simple cycles.
Castro, Sofia, Lohse, Alexander
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Electronic Journal of Qualitative Theory of Differential Equations, 2017 In this work, we analyze a bi-dimensional differential equation system obtained by considering Holling type II functional response in prey–predator model with strong Allee effect in prey.
Partha Mandal, Aadil Lahrouz
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Complexity, Volume 2026, Issue 1, 2026.This study investigates a discrete‐time predator–prey model that includes both prey refuge and memory effects. The research identifies the conditions under which fixed points exist and remain stable. A key focus is placed on analyzing different types of bifurcation—such as period doubling (PD), Neimark–Sacker (NS), and strong resonances (1 : 2, 1 : 3 ...
S. M. Sohel Rana +2 more
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Network Inoculation: Heteroclinics and phase transitions in an epidemic model [PDF]
, 2016 In epidemiological modelling, dynamics on networks, and in particular adaptive and heterogeneous networks have recently received much interest. Here we present a detailed analysis of a previously proposed model that combines heterogeneity in the ...
Anderson R. M. +7 more
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Pattern Formation and Nonlinear Waves Close to a 1:1 Resonant Turing and Turing–Hopf Instability
Studies in Applied Mathematics, Volume 155, Issue 5, November 2025.ABSTRACT In this paper, we analyze the dynamics of a pattern‐forming system close to simultaneous Turing and Turing–Hopf instabilities, which have a 1:1 spatial resonance, that is, they have the same critical wave number. For this, we consider a system of coupled Swift–Hohenberg equations with dispersive terms and general, smooth nonlinearities.
Bastian Hilder, Christian Kuehn
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Stability and bifurcations of heteroclinic cycles of type Z
, 2012 Dynamical systems that are invariant under the action of a non-trivial symmetry group can possess structurally stable heteroclinic cycles. In this paper we study stability properties of a class of structurally stable heteroclinic cycles in R^n which we ...
Podvigina, Olga
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