Abstract
Most physical phenomena are modeled as continuous or discrete dynamic systems of a second dimension or more, but because of the multiplicity of bifurcation parameters and the large dimension, researchers have big problems for the study of this type of systems. For this reason, this article proposes a new method that facilitates the qualitative study of continuous dynamic systems of three dimensions in general and chaotic systems in particular, which contains many parameters of bifurcations. This method is based on projection on the plane and on an appropriate bifurcation parameter.
Highlights
The theory of chaos is one of the few, one of the very few mathematical theories that has had any real media success
The purpose of this article is to provide a new method for studying continuous three-dimensional dynamic systems with several bifurcation parameters [1]
1 1 According to the Hopf bifurcation theorem, it can be concluded that a0 is the critical value
Summary
The theory of chaos is one of the few, one of the very few mathematical theories that has had any real media success. The purpose of this article is to provide a new method for studying continuous three-dimensional dynamic systems with several bifurcation parameters [1]. This method gives important results on dynamic behavior, stability, bifurcations and chaos. This method has two steps, a projection on the plane to obtain a dynamic system of a smaller dimension, the choice of the appropriate parameter. A subsystem of the original system will be studied via an analysis of its dynamic behavior using a lower dimension (2D). This will be useful in the final study of the dynamic behavior of the original system
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