scholarly journals Weak Equivalence Transformations for a Class of Models in Biomathematics

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Igor Leite Freire ◽  
Mariano Torrisi
Keyword(s):  
Population Dynamics ◽  
Aedes Aegypti ◽  
Lie Algebra ◽  
Reaction Diffusion ◽  
Weak Equivalence ◽  
Equivalence Transformations ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Population Dynamics Models ◽  
Dynamics Models

A class of reaction-diffusion systems unifying severalAedes aegyptipopulation dynamics models is considered. Equivalence transformations are found. Extensions of the principal Lie algebra are derived for some particular cases.

scholarly journals Lie Symmetries and Solutions of Reaction Diffusion Systems Arising in Biomathematics

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1530
Author(s):  
Mariano Torrisi ◽  
Rita Traciná
Keyword(s):  
Population Dynamics ◽  
Mathematical Models ◽  
Lie Algebra ◽  
Reaction Diffusion ◽  
Equivalence Transformation ◽  
Transformation Groups ◽  
Weak Equivalence ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Special Solutions

In this paper, a special subclass of reaction diffusion systems with two arbitrary constitutive functions Γ(v) and H(u,v) is considered in the framework of transformation groups. These systems arise, quite often, as mathematical models, in several biological problems and in population dynamics. By using weak equivalence transformation the principal Lie algebra, LP, is written and the classifying equations obtained. Then the extensions of LP are derived and classified with respect to Γ(v) and H(u,v). Some wide special classes of special solutions are carried out.

scholarly journals A review on symmetries for certain Aedes aegypti models

2015 ◽  
Vol 38 ◽  
pp. 1560073
Author(s):  
Igor Leite Freire ◽  
Mariano Torrisi
Keyword(s):  
Aedes Aegypti ◽  
Reaction Diffusion ◽  
Weak Equivalence ◽  
Invariant Solutions ◽  
General Reaction ◽  
Equivalence Transformations ◽  
Reaction Diffusion Systems ◽  
Group Invariant ◽  
Diffusion Systems ◽  
Group Invariant Solutions

We summarize our results related with mathematical modeling of Aedes aegypti and its Lie symmetries. Moreover, some explicit, group-invariant solutions are also shown. Weak equivalence transformations of more general reaction diffusion systems are also considered. New classes of solutions are obtained.

scholarly journals A structural approach to control of transitional waves of nonlinear diffusion-reaction systems: Theory and possible applications to bio-medicine

2002 ◽  
Vol 7 (1) ◽  
pp. 27-40 ◽  
Author(s):  
Victor Kardashov ◽  
Shmuel Einav
Keyword(s):  
Nonlinear Diffusion ◽  
Structural Parameters ◽  
Deterministic Chaos ◽  
Reaction Diffusion ◽  
Diffusion Reaction ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Novel Approach ◽  
Dynamics Models ◽  
And Control

This paper has considered a novel approach to structural recognition and control of nonlinear reaction-diffusion systems (systems with density dependent diffusion). The main consistence of the approach is interactive variation of the nonlinear diffusion and sources structural parameters that allows to implement a qualitative control and recognition of transitional system conditions (transients). The method of inverse solutions construction allows formulating the new analytic conditions of compactness and periodicity of the transients that is also available for nonintegrated systems. On the other hand, using of energy conservations laws, allows transfer to nonlinear dynamics models that gives the possiblity to apply the modern deterministic chaos theory (particularly the Feigenboum's universal constants and scenario of chaotic transitions).

EPIDEMIC REACTION-DIFFUSION SYSTEM WITH CROSS-DIFFUSION: MODELING AND NUMERICAL SOLUTION

1995 ◽  
Vol 03 (03) ◽  
pp. 733-746 ◽  
Author(s):  
V. CAPASSO ◽  
A. DI LIDDO ◽  
F. NOTARNICOLA ◽  
L. RUSSO
Keyword(s):  
Population Dynamics ◽  
Numerical Analysis ◽  
Numerical Solution ◽  
Reaction Diffusion ◽  
Diffusion System ◽  
Diffusion Modeling ◽  
Qualitative Behaviour ◽  
Reaction Diffusion Systems ◽  
Cross Diffusion ◽  
Diffusion Systems

Reaction-diffusion systems with cross-diffusion are analyzed here for modeling the population dynamics of epidemic systems. In this paper specific attention is devoted to the numerical analysis and simulation of such systems to show that, far from possible pathologies, the qualitative behaviour of the systems may well interpret the dynamics of real systems.

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