Nonlinear dynamical systems seen through the scope of the Quasi-polynomial theory

e-Boletim da Física

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Title Nonlinear dynamical systems seen through the scope of the Quasi-polynomial theory
 
Creator Brenig, Léon
 
Subject
 
Description A unified theory of nonlinear dynamical systems is presented. The unification relies on the Quasi-polynomial approach of these systems. The main result of this approach is that most nonlinear dynamical systems can be exactly transformed to a unique format, the Lotka-Volterra system. An abstract Lie algebraic structure underlying most nonlinear dynamical systems is found. This structure, based on two sets of operators obeying specific commutation rules and on a Hamiltonian expressed in terms of these operators, bears a strong similarity with the fundamental algebra of quantum physics.From these properties, two forms of the exact general solution can be constructed for all Lotka-Volterra systems. One of them corresponds to a Taylor series in power of time. In contrast with other Taylor series solutions methods for nonlinear dynamical systems, our approach provides the exact analytic form of the general coefficient of that series. The second form of the solution is given in terms of a path integral. These solutions can be transformed back to solutions of the general nonlinear dynamical systems.
 
Publisher e-Boletim da Física
 
Contributor
 
Date 2016-11-30
 
Type info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion

 
Format application/pdf
 
Identifier http://periodicos.unb.br/index.php/e-bfis/article/view/21367
 
Source e-Boletim da Física; v. 5, n. 1 (2016)
2318-8901
 
Language por
 
Relation http://periodicos.unb.br/index.php/e-bfis/article/view/21367/15310
 
Rights Direitos autorais 2016 e-Boletim da Física
 

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