Predicting noise-induced critical transitions in bistable systems

Ma, Jinzhong; Xu, Yong; Li, Yongge; Tian, Ruilan; Kurths, Jürgen

doi:10.1063/1.5115348

Cited by 43 publications

(19 citation statements)

References 46 publications

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“…Sources of noise may affect our reported results in several ways: (i) stable equilibria may be preserved with the presence of high-frequency fluctuations; (ii) noise may induce transitions between stable states in the bistable scenarios. 65 These noise-induced critical transitions may depend upon the hyperbolicity of equilibria (i.e., how attracting they are) and on the size of their basins of attraction. (iii) Noise-induced extinctions (see, e.g., Ref.…”

Section: Discussionmentioning

confidence: 99%

Host–virus evolutionary dynamics with specialist and generalist infection strategies: Bifurcations, bistability, and chaos

Nurtay

Hennessy

Alsedà

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this work, we have investigated the evolutionary dynamics of a generalist pathogen, e.g., a virus population, that evolves toward specialization in an environment with multiple host types. We have particularly explored under which conditions generalist viral strains may rise in frequency and coexist with specialist strains or even dominate the population. By means of a nonlinear mathematical model and bifurcation analysis, we have determined the theoretical conditions for stability of nine identified equilibria and provided biological interpretation in terms of the infection rates for the viral specialist and generalist strains. By means of a stability diagram, we identified stable fixed points and stable periodic orbits, as well as regions of bistability. For arbitrary biologically feasible initial population sizes, the probability of evolving toward stable solutions is obtained for each point of the analyzed parameter space. This probability map shows combinations of infection rates of the generalist and specialist strains that might lead to equal chances for each type becoming the dominant strategy. Furthermore, we have identified infection rates for which the model predicts the onset of chaotic dynamics. Several degenerate Bogdanov-Takens and zero-Hopf bifurcations are detected along with generalized Hopf and zero-Hopf bifurcations. This manuscript provides additional insights into the dynamical complexity of host-pathogen evolution toward different infection strategies.

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Section: Discussionmentioning

confidence: 99%

Host–virus evolutionary dynamics with specialist and generalist infection strategies: Bifurcations, bistability, and chaos

Nurtay

Hennessy

Alsedà

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…where, We have calculated SSPD numerically using finite difference method [39] with step size 0.001. In Fig.…”

Section: Fokker-planck Equationsmentioning

confidence: 99%

The Role of Harvesting in Population Control in Presence of Multiple Stochastic Noise Sources

Mandal¹,

Jana²,

Poria

2021

Preprint

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In this paper, we compare the role of constant and Michaelis-Menten type harvesting in single species population control in presence of stochastic noises sources. Steady state probability distributions and stationary potentials of the population for the two types of harvesting are determined by Fokker-Planck equations. Stochastic bifurcation analysis and mean first passage times have been computed. Noise induced critical transitions are observed depending on the strength of the noises. The extinction possibility of population in stochastic control with Michaelis-Menten type harvesting is higher than the constant rate of harvesting. One of the findings is the transition of the population from bistable to tristable for weak noise and Michaelis-Menten type harvesting. Another finding is noise enhanced stability phenomenon for negatively correlated noises. In case of population control, constant rate of harvesting is better in deterministic case whereas Michaelis-Menten type harvesting is better in stochastic case. The stochastic control is more efficient than deterministic control as average population size in stochastic case is lower than the deterministic case. The results obtained in this study can throw light on toxic phytoplankton blooms and its control in marine ecosystem. Moreover, the study can be useful to explain wild prey population outbreak and its control in deep forest.

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“…Similar to the method in Ref. [3], the absorbed regions corresponding to CT 1, CT 2, and CT 3 are also defined here via the relationship between the tangent slope of P i (x) and the slope of a given line in the xP i (x)-plane. It should be noted that, in the following, α = 1.5, β = −1, σ = 0.8, and d = 0.1 are taken as a set of basic parameter values.…”

Section: Absorbed Regionmentioning

confidence: 99%

“…Critical transition (CT) also called tipping, a phenomenon that a system shifts from one state to another contrasting one, is ubiquitous in many health and climate systems [1][2][3][4] . This sudden and often irreversible change may cause significant impacts on the local economy or society.…”

Section: Introductionmentioning

confidence: 99%

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Quantifying the parameter dependent basin of the unsafe regime of asymmetric Lévy-noise-induced critical transitions

et al. 2020

Appl. Math. Mech.-Engl. Ed.

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In real systems, the unpredictable jump changes of the random environment can induce the critical transitions (CTs) between two non-adjacent states, which are more catastrophic. Taking an asymmetric Lévy-noise-induced tri-stable model with desirable, sub-desirable, and undesirable states as a prototype class of real systems, a prediction of the noise-induced CTs from the desirable state directly to the undesirable one is carried out. We first calculate the region that the current state of the given model is absorbed into the undesirable state based on the escape probability, which is named as the absorbed region. Then, a new concept of the parameter dependent basin of the unsafe regime (PDBUR) under the asymmetric Lévy noise is introduced. It is an efficient tool for approximately quantifying the ranges of the parameters, where the noise-induced CTs from the desirable state directly to the undesirable one may occur. More importantly, it may provide theoretical guidance for us to adopt some measures to avert a noise-induced catastrophic CT.

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Predicting noise-induced critical transitions in bistable systems

Cited by 43 publications

References 46 publications

Host–virus evolutionary dynamics with specialist and generalist infection strategies: Bifurcations, bistability, and chaos

Host–virus evolutionary dynamics with specialist and generalist infection strategies: Bifurcations, bistability, and chaos

The Role of Harvesting in Population Control in Presence of Multiple Stochastic Noise Sources

Quantifying the parameter dependent basin of the unsafe regime of asymmetric Lévy-noise-induced critical transitions

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