Stochastic dynamics and logistic population growth

Méndez, Vicenç; Assaf, Michael; Campos, Daniel; Horsthemke, Werner

doi:10.1103/physreve.91.062133

Cited by 17 publications

(11 citation statements)

References 58 publications

(88 reference statements)

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“…In either case, we have twice as many unknowns as the number of values of q ij included in the sum in Eq. (22). Note that the left hand side of the equation system is the same for both incident polarizations, and will also remain the same for all angles of incidence, as k only enters at the right hand side of Eq.…”

Section: Numerical Solution Of the Reduced Rayleigh Equationmentioning

confidence: 99%

“…Note that the left hand side of the equation system is the same for both incident polarizations, and will also remain the same for all angles of incidence, as k only enters at the right hand side of Eq. (22).…”

Section: Numerical Solution Of the Reduced Rayleigh Equationmentioning

confidence: 99%

“…Since the initial publication of these seminal works, numerous studies on wave scattering from randomly rough surfaces have appeared in the literature [13][14][15][16][17][18][19], and several new multiple scattering phenomena have been predicted and confirmed experimentally. These phenomena include the enhanced backscattering and enhanced transmission phenomena, the satellite peak phenomenon, and coherent effects in the intensity-intensity correlation functions [19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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Numerical simulations of scattering of light from two-dimensional rough surfaces using the reduced Rayleigh equation

Nordam¹,

Letnes²,

Simonsen³

2013

Front. Physics

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A formalism is introduced for the non-perturbative, purely numerical, solution of the reduced Rayleigh equation (RRE) for the scattering of light from two-dimensional penetrable rough surfaces. Implementation and performance issues of the method, and various consistency checks of it, are presented and discussed. The proposed method is found, within the validity of the Rayleigh hypothesis, to give reliable results. For a nonabsorbing metal surface the conservation of energy was explicitly checked, and found to be satisfied to within 0.03%, or better, for the parameters assumed. This testifies to the accuracy of the approach and a satisfactory discretization. As an illustration, we calculate the full angular distribution of the mean differential reflection coefficient for the scattering of p-or s-polarized light incident on two-dimensional dielectric or metallic randomly rough surfaces defined by (isotropic or anisotropic) Gaussian and cylindrical power spectra. Simulation results obtained by the proposed method agree well with experimentally measured scattering data taken from similar well-characterized, rough metal samples, or to results obtained by other numerical methods.

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Section: Numerical Solution Of the Reduced Rayleigh Equationmentioning

confidence: 99%

Section: Numerical Solution Of the Reduced Rayleigh Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical simulations of scattering of light from two-dimensional rough surfaces using the reduced Rayleigh equation

Nordam¹,

Letnes²,

Simonsen³

2013

Front. Physics

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“…When λ = 0, the second reaction vanishes and the theta-logistic equation is obtained in the mean field limit [28]. When β = 0, the last reaction vanishes and the logistic equation is recovered in the mean field limit [29].…”

Section: Stochastic Individual-based Model With Allee Effectmentioning

confidence: 99%

Demographic stochasticity and extinction in populations with Allee effect

et al. 2019

Self Cite

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We study simple stochastic scenarios, based on birth-and-death Markovian processes, that describe populations with Allee effect, to account for the role of demographic stochasticity. In the meanfield deterministic limit we recover well-known deterministic evolution equations widely employed in population ecology. The mean-time to extinction is in general obtained by the Wentzel-Kramers-Brillouin (WKB) approximation for populations with strong and weak Allee effects. An exact solution for the mean time to extinction can be found via a recursive equation for special cases of the stochastic dynamics. We study the conditions for the validity of the WKB solution and analyze the boundary between the weak and strong Allee effect by comparing exact solutions with numerical simulations.

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“…However, the motivation behind all the governing equations therein is rather phenomenological. In the light of the existing literature on microscopic stochastic birth-death process [34][35][36] leading to replicator equation in the mean field limit and that on the microscopic process leading similarly to deterministic population dynamics equation (e.g., logistic equation [37]), in this paper we are motivated to derive the macroscopic model of the game-environment feedback dynamics starting from a microscopic multidimensional birth-death process that incorporates the feedback between the evolutionary system and an ecological self-renewing resource. Furthermore, this endeavour automatically facilitates the study of finite sized population with a finite carrying capacity which is known to have quite non-trivial counter-intuitive effects [38].…”

Section: Introductionmentioning

confidence: 99%

Eco-evolutionary games for harvesting self-renewing common resource: Effect of growing harvester population

Bairagya¹,

Mondal²,

Chowdhury³

et al. 2022

Preprint

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The tragedy of the commons (TOC) is a ubiquitous social dilemma witnessed in interactions between a population of living entities and shared resources available to them: The individuals in the population tend to selfishly overexploit a common resource as it is arguably the rational choice, or in case of non-human beings, it may be an evolutionarily uninvadable action. How to avert the TOC is a significant problem related to the conservation of resources. It is not hard to envisage situations where the resource could be self-renewing and the size of the population may be dependent on the state of the resource through the fractions of the population employing different exploitation rates. If the self-renewal rate of the resource lies between the maximum and the minimum exploitation rates, it is not a priori obvious under what conditions the TOC can be averted. In this paper, we address this question analytically and numerically using the setup of an evolutionary game theoretical replicator equation that models the Darwinian tenet of natural selection. Through the replicator equation, while we investigate how a population of replicators exploit the shared resource, the latter's dynamical feedback on the former is also not ignored. We also present a transparent bottom-up derivation of the game-resource feedback model to facilitate future studies on the stochastic effects on the findings presented herein.

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Stochastic dynamics and logistic population growth

Cited by 17 publications

References 58 publications

Numerical simulations of scattering of light from two-dimensional rough surfaces using the reduced Rayleigh equation

Numerical simulations of scattering of light from two-dimensional rough surfaces using the reduced Rayleigh equation

Demographic stochasticity and extinction in populations with Allee effect

Eco-evolutionary games for harvesting self-renewing common resource: Effect of growing harvester population

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