Critical slowing down close to a global bifurcation of a curve of quasi-neutral equilibria

Fontich, Ernest; Guillamón, Antoni; Lázaro, J. Tomás; Alarcón, Tomás; Vidiella, Blai; Sardanyés, Josep

doi:10.1016/j.cnsns.2021.106032

Cited by 4 publications

(1 citation statement)

References 53 publications

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“…The main purpose of this article, motivated by [16,[38][39][40][41][42][43][44] and others, is to provide a further discussion to obtain the global bifurcation structure with detailed illustration. If we think of nonlinear prey-taxis as a bifurcation parameter, the proof of the existence of bifurcation will be offered from a simple eigenvalue.…”

Section: Introductionmentioning

confidence: 99%

Global bifurcation for a Beddington–DeAngelis and Tanner predator–prey reaction–diffusion system with prey‐taxis

Luo,

Wang

2023

Math Methods in App Sciences

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The aim of this paper is to establish a precise illustration for the structure of the nonconstant steady states for a Beddington–DeAngelis and Tanner predator–prey reaction–diffusion system with prey‐taxis. We treat the nonlinear prey‐taxis as a bifurcation parameter to analyze the bifurcation structure of the system. Furthermore, the exported global bifurcation theorem, under a rather natural condition, offers the existence of nonconstant steady states. In the proof, a priori estimates of steady states will play an important role. The local stability analysis with a numerical simulation and bifurcation analysis are given. Finally, some conclusions including biological meanings are performed to summarize our main analytic results and future investigations.

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Section: Introductionmentioning

confidence: 99%

Global bifurcation for a Beddington–DeAngelis and Tanner predator–prey reaction–diffusion system with prey‐taxis

Luo,

Wang

2023

Math Methods in App Sciences

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Early warning signals of complex critical transitions in deterministic dynamics

Evers,

Borsboom,

Fried

et al. 2024

Nonlinear Dyn

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Early Warning Signals (EWS) have generated much excitement for their potential to anticipate transitions in various systems, ranging from climate change in ecology to disease staging in medicine. EWS hold particular promise for bifurcations, a transition mechanism in which a smooth, gradual change in a control parameter of the system results in a rapid change in system dynamics. The predominant reason to expect EWS is because many bifurcations are preceded by Critical Slowing Down (CSD): if assuming the system is subject to continuous, small, Gaussian noise, the system is slower to recover from perturbations closer to the transition. However, this focus on warning signs generated by stochasticity has overshadowed warning signs which may already be found in deterministic dynamics. This is especially true for higher-dimensional systems, where more complex attractors with intrinsic dynamics such as oscillations not only become possible—they are increasingly more likely. The present study focuses on univariate and multivariate EWS in deterministic dynamics to anticipate complex critical transitions, including the period-doubling cascade to chaos, chaos-chaos transitions, and the extinction of a chaotic attractor. In a four-dimensional continuous-time Lotka–Volterra model, EWS perform well for most bifurcations, even with lower data quality. The present study highlights three reasons why EWS may still work in the absence of CSD: changing attractor morphology (size, shape, and location in phase space), shifting power spectra (amplitude and frequency), and chaotic transitional characteristics (density across attractor). More complex attractors call for different warning detection methods to utilise warning signs already contained within purely deterministic dynamics.

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Quasineutral multistability in an epidemiological-like model for defective-helper betacoronavirus infection in cell cultures

Muñoz-Sánchez,

Lázaro,

Hillung

et al. 2025

Applied Mathematical Modelling

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Critical slowing down close to a global bifurcation of a curve of quasi-neutral equilibria

Cited by 4 publications

References 53 publications

Global bifurcation for a Beddington–DeAngelis and Tanner predator–prey reaction–diffusion system with prey‐taxis

Global bifurcation for a Beddington–DeAngelis and Tanner predator–prey reaction–diffusion system with prey‐taxis

Early warning signals of complex critical transitions in deterministic dynamics

Quasineutral multistability in an epidemiological-like model for defective-helper betacoronavirus infection in cell cultures

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