Dynamics of interspecific <i>k</i> species competition model

Mathew, Smitha Mary; Dilip, D. S.

doi:10.1080/09720502.2021.2012891

Cited by 4 publications

(4 citation statements)

References 20 publications

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“…Theoretical ecology relies heavily on mathematical models of competition. Several mathematical models have been suggested to date to characterize the growth of contending populations; some of them are detailed in [50][51][52], including discrete-time models [53,54]. The wide range of biological factors that influence ecosystem behavior makes it difficult for researchers to come to a consensus on how to simulate the dynamics of competing populations.…”

Section: Ricker's Modelmentioning

confidence: 99%

“…Ricker's model is often used to explain the dynamics of two populations that are linked through migrations [50][51][52][53][54][55][56][57][58]. As a result, nothing is known about how Ricker communities evolved.…”

Section: Ricker's Modelmentioning

confidence: 99%

“…Assume that after the ðk − 1Þ-th time step MCMC procedure, M samples (i.e., particles) [48][49][50][51][52][53][54][55][56][57][58][59][60]. This results in the estimated density p Mix ðΩ, m k−1 jy 1:k−1 Þ based on GMMs.…”

Section: An Augmented Sequential Markov Chain Monte Carlo Algorithmmentioning

confidence: 99%

“…This results in the estimated density p Mix ðΩ, m k−1 jy 1:k−1 Þ based on GMMs. The methodology developed and implemented in [48][49][50][51][52][53][54][55][56][57][58][59][60] ensures that the fitted GMM is close to the true posterior density pðΩ,…”

Section: An Augmented Sequential Markov Chain Monte Carlo Algorithmmentioning

confidence: 99%

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Embedded Estimation Sequential Bayes Parameter Inference for the Ricker Dynamical System

et al. 2022

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The dynamical systems are comprised of two components that change over time: the state space and the observation models. This study examines parameter inference in dynamical systems from the perspective of Bayesian inference. Inference on unknown parameters in nonlinear and non-Gaussian dynamical systems is challenging because the posterior densities corresponding to the unknown parameters do not have traceable formulations. Such a system is represented by the Ricker model, which is a traditional discrete population model in ecology and epidemiology that is used in many fields. This study, which deals with parameter inference, also known as parameter learning, is the central objective of this study. A sequential embedded estimation technique is proposed to estimate the posterior density and obtain parameter inference. The resulting algorithm is called the Augmented Sequential Markov Chain Monte Carlo (ASMCMC) procedure. Experiments are performed via simulation to illustrate the performance of the ASMCMC algorithm for observations from the Ricker dynamical system.

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Section: Ricker's Modelmentioning

confidence: 99%

Section: Ricker's Modelmentioning

confidence: 99%

Section: An Augmented Sequential Markov Chain Monte Carlo Algorithmmentioning

confidence: 99%

Section: An Augmented Sequential Markov Chain Monte Carlo Algorithmmentioning

confidence: 99%

See 2 more Smart Citations

Embedded Estimation Sequential Bayes Parameter Inference for the Ricker Dynamical System

et al. 2022

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Stability and Bifurcation Analysis of Two Spatial Population Dynamics Models

Dilip

Philip

2022

Int. J. Appl. Comput. Math

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Behavior of solutions of a discrete population model with mutualistic interaction

Babu,

Dilip,

Mathew

2024

Computational and Mathematical Biophysics

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We focus on the stability analysis of two types of discrete dynamic models: a discrete dynamic equation and a discrete dynamics system consisting of two equations with mutualistic interaction given by x n + 1 = a + b x n λ − ( x n − 1 + x n − k ) c + x n − 1 + x n − k {x}_{n+1}=a+\frac{b{x}_{n}{\lambda }^{-\left({x}_{n-1}+{x}_{n-k})}}{c+{x}_{n-1}+{x}_{n-k}} and x n + 1 = a 1 + b 1 y n λ − ( y n − 1 + x n − k ) c 1 + y n − 1 + x n − k , y n + 1 = a 2 + b 2 x n λ − ( x n − 1 + y n − k ) c 2 + x n − 1 + y n − k , {x}_{n+1}={a}_{1}+\frac{{b}_{1}{y}_{n}{\lambda }^{-({y}_{n-1}+{x}_{n-k})}}{{c}_{1}+{y}_{n-1}+{x}_{n-k}},\hspace{1.0em}{y}_{n+1}={a}_{2}+\frac{{b}_{2}{x}_{n}{\lambda }^{-\left({x}_{n-1}+{y}_{n-k})}}{{c}_{2}+{x}_{n-1}+{y}_{n-k}}, respectively, where k ∈ { 2 , 3 , … } k\in \left\{2,3,\ldots \right\} , the constants a , a 1 , ≥ 0 a,{a}_{1},\ge 0 , b , b 1 > 0 b,{b}_{1}\gt 0 , and c , c 1 ≥ 0 c,{c}_{1}\ge 0 be the initial densities, finite rate of increase and the limiting constant associated with the density of the species, respectively, and a 2 ≥ 0 {a}_{2}\ge 0 , b 2 > 0 {b}_{2}\gt 0 , and c 2 ≥ 0 {c}_{2}\ge 0 be the initial densities, finite rate of increase, and the limiting constant associated with the density of the mutually interacting species, respectively. k k , a positive integer represents a time delay in the system and λ ≥ 1 \lambda \ge 1 shows a decay factor based on the sum of two past time step population densities. Our main objective is to understand the impact of mutualistic interactions on the stability of discrete dynamic systems. To illustrate the boundedness and stability of these models, we also provide animated plots and bifurcation diagrams.

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Dynamics of interspecific k species competition model

Cited by 4 publications

References 20 publications

Embedded Estimation Sequential Bayes Parameter Inference for the Ricker Dynamical System

Embedded Estimation Sequential Bayes Parameter Inference for the Ricker Dynamical System

Stability and Bifurcation Analysis of Two Spatial Population Dynamics Models

Behavior of solutions of a discrete population model with mutualistic interaction

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