Lie Symmetry of the Diffusive Lotka–Volterra System with Time-Dependent Coefficients

Davydovych, Vasyl’

doi:10.3390/sym10020041

Cited by 4 publications

(6 citation statements)

References 30 publications

(33 reference statements)

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“…[Rate of changes of v] = − [net rate of loss of v without prey] + [net rate of growth of v due to predation]. [11] To explain chemical reactions that have periodic behaviour in chemical concentrations Lokta suggested the same model. As a result, system (1) is referred to be the Lokta -Volterra model.…”

Section: [Rate Of Changes Of U]mentioning

confidence: 99%

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Solving Model of Reaction-Diffusion System in Ecological by Symmetry Lie Group Methods

Omar,

I. Sadeeq,

T. Sarhan

2023

wjps

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In this paper, we will use analytical methods for solving the fundamental element of a reaction diffusion model in ecology. The model denotes an interaction between two species which describe ecological predations, and mathematically is defined as a system of partial differential equations with initial and boundary conditions. Symmetry Lie group methods are used to transform this model into a system of ordinary differential equations, then this system solved by generalized tanh function method when there exists a small parameter appear in one of the equation.

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Section: [Rate Of Changes Of U]mentioning

confidence: 99%

“…As a result, system (1) is referred to be the Lokta -Volterra model. [11]. The most crucial method for solving nonlinear issues is a symmetry group analysis based on the transformation group, now known as lie groups.…”

Section: [Rate Of Changes Of U]mentioning

confidence: 99%

Solving Model of Reaction-Diffusion System in Ecological by Symmetry Lie Group Methods

Omar,

I. Sadeeq,

T. Sarhan

2023

wjps

View full text Add to dashboard Cite

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“…Scaling X, we can assume that a 1 = 1. Then X changes to the case (7). If a 1 , a 2 , a 3 = 0 then one can vanish the coefficients of X 3 by setting s 1 = a 5 a 1 , s 2 = − a 5 a 2 and s 3 = s 5 = 0.…”

Section: The Optimal System Of One Dimension Subalgebrasmentioning

confidence: 99%

“…The diffusion equation is one of the well-known equations with many applications in engineering problems, heat conduction, chemical diffusion, fluid flow, mass transfer, refrigeration, and traffic analysis, and so on, [7,15,30]. Recently, the study of fractional ordinary differential equation and the partial differential equation has attracted much attention due to an exact description of differential equations in fluid mechanics, biology, physics, engineering, and other areas of science [14,42,44].…”

Section: Introductionmentioning

confidence: 99%

Lie symmetries reduction and spectral methods on the fractional two-dimensional heat equation

Bakhshandeh-Chamazkoti¹,

Akbari²

2022

Preprint

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In this paper, the Lie symmetry analysis is proposed for a space-time convection-diffusion fractional differential equations with the Riemann-Liouville derivative by (2+1) independent variables and one dependent variable. We find a reduction form of our governed fractional differential equation using the similarity solution of our Lie symmetry. One-dimensional optimal system of Lie symmetry algebras is found. We present a computational method via the spectral method based on Bernstein's operational matrices to solve the two-dimensional fractional heat equation with some initial conditions.

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“…In fundamental physics, geometrical formulations have been used with great success to construct, analyse and validate models [8]. Existing applications of symmetry methods in mathematical biology, reviewed in [9], include finding analytical solutions to reaction-diffusion models [10,11,12],…”

Section: Introductionmentioning

confidence: 99%

Symmetries of systems of first order ODEs: Symbolic symmetry computations, mechanistic model construction and applications in biology

Borgqvist¹,

Ohlsson²,

Baker³

2022

Preprint

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We discuss the role and merits of symmetry methods for the analysis of biological systems. In particular, we consider systems of first order ordinary differential equations and provide a comprehensive review of the geometrical foundations pertinent to symmetries of such systems. Subsequently, we present an algorithm for finding infinitesimal generators of symmetries for systems with rational reaction terms, and an open-source implementation of the algorithm using symbolic computations. We discuss two complementary perspectives on symmetries in mechanistic modelling; as tools for the analysis of a given model or as a geometrical principle for incorporating biological properties in the construction of new models. Through numerous examples of relevance to modelling in biology we demonstrate the different uses of symmetry methods, and also discuss how to infer symmetries from experimental data.

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Lie Symmetry of the Diffusive Lotka–Volterra System with Time-Dependent Coefficients

Cited by 4 publications

References 30 publications

Solving Model of Reaction-Diffusion System in Ecological by Symmetry Lie Group Methods

Solving Model of Reaction-Diffusion System in Ecological by Symmetry Lie Group Methods

Lie symmetries reduction and spectral methods on the fractional two-dimensional heat equation

Symmetries of systems of first order ODEs: Symbolic symmetry computations, mechanistic model construction and applications in biology

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