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Dynamics in diffusive Leslie–Gower prey–predator model with weak diffusion
Nonlinear Analysis, 2022 This paper is concerned with the diffusive Leslie–Gower prey–predator model with weak diffusion. Assuming that the diffusion rates of prey and predator are sufficiently small and the natural growth rate of prey is much greater than that of predators ...
Xiao Wu, Mingkang Ni
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Emerging criticality at bifurcation points in heteroclinic dynamics
Physical Review Research, 2020 Heteroclinic dynamics is a suitable framework to describe transient dynamics that is characteristic for ecological as well as neural systems, in particular for cognitive processes.
Maximilian Voit +1 more
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Fear Effect on a Predator–Prey Model with Non-Differential Fractional Functional Response
Fractal and Fractional, 2023 In this paper, we study the factor of the fear effect in a predator–prey model with prey refuge and a non-differentiable fractional functional response due to the group defense.
Salam Mohammed Ghazi Al-Mohanna +1 more
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Quasiperiodic, periodic, and slowing-down states of coupled heteroclinic cycles [PDF]
, 2012 We investigate two coupled oscillators, each of which shows an attracting heteroclinic cycle in the absence of coupling. The two heteroclinic cycles are nonidentical. Weak coupling can lead to the elimination of the slowing-down state that asymptotically
Cross, M. C. +3 more
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Chaos criteria and chaotification schemes on a class of first-order partial difference equations
Mathematical Biosciences and Engineering, 2023 This article is involved in chaos criteria and chaotification schemes on one kind of first-order partial difference equations having non-periodic boundary conditions.
Zongcheng Li , Jin Li
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Scalar Field Evolution at Background and Perturbation Levels for a Broad Class of Potentials
Fortschritte der Physik, Volume 71, Issue 10-11, November 2023., 2023 Abstract In this paper, a non‐interacting scalar field cosmology with an arbitrary potential using the f‐deviser method that relies on the differentiability properties of the potential is investigated. Using this alternative mathematical approach, a unified dynamical system analysis at a scalar field's background and perturbation levels with arbitrary ...
Genly Leon +5 more
wiley +1 more source
Global bifurcations close to symmetry [PDF]
, 2016 Heteroclinic cycles involving two saddle-foci, where the saddle-foci share both invariant manifolds, occur persistently in some symmetric differential equations on the 3-dimensional sphere.
Labouriau, Isabel S. +1 more
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Building modern coexistence theory from the ground up: The role of community assembly
Ecology Letters, Volume 26, Issue 11, Page 1840-1861, November 2023., 2023 Modern coexistence theory (MCT) is limited by its dependence on the naive invasion growth rate criterion. We extend the applicability of MCT by using permanence theory. We use this newly developed method to gain new insights into community coexistence and its limits.
Jurg W. Spaak, Sebastian J. Schreiber
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Almost complete and equable heteroclinic networks [PDF]
, 2019 Heteroclinic connections are trajectories that link invariant sets for an autonomous dynamical flow: these connections can robustly form networks between equilibria, for systems with flow-invariant spaces.
Ashwin, Peter +2 more
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Beltrami fields and knotted vortex structures in incompressible fluid flows
Bulletin of the London Mathematical Society, Volume 55, Issue 3, Page 1059-1103, June 2023., 2023 Abstract This paper gives a survey on recent results about the existence of knotted vortex structures in incompressible fluids. This includes the proof of Lord Kelvin's conjecture on the existence of knotted vortex tubes in steady Euler flows and a new probabilistic approach to address Arnold's speculation that typical Beltrami fields should exhibit ...
Alberto Enciso, Daniel Peralta‐Salas
wiley +1 more source