| Volume 14, Number 4, 2024, Pages - DOI：10.11948/JAAC-2023-0308 |
| Extended Center Manifold, Global Bifurcation and Approximate Solutions of Chen chaotic dynamical system |
| Mohamed Tantawy,Hamdy I. Abdel-Gawad,Basma Abdel-Aziz |
| Keywords:Chen dynamical system Global bifurcation Extended center manifold Approximate analytical solutions. |
| Abstract: |
| The study of the chaotic Chen dynamic System (CDS) has been a recent focus in the literature,
with numerous works exploring its various chaotic features. However, the majority of
these studies have relied primarily on numerical techniques to investigate nonlinear dynamic
systems (NLDSs). In this context, our aim is to derive approximate analytical solutions for
the CDS by developing an iterative scheme. We have proven the convergence theorem for this
scheme, which ensures that our iterative process will converge to the exact solution. Additionally,
we introduce a new method for constructing the extended center manifold, a critical
component in the analysis of dynamical systems. The characteristics of the global bifurcation
of the system components within the parameter space are explored. The error analysis of the
iterated solutions demonstrates the efficiency of the present technique. We present both three-dimensional
(3D) and two-dimensional (2D) phase portraits of the system. The 3D portrait
reveals a feedback loop pattern, while the 2D portrait, which represents the interaction of the
system components, exhibits multiple pools and cross pools. Furthermore, we illustrate the
global bifurcation by visualizing the components of the CDS against the space parameters.
The sensitivity of CDS to in nitesimal variations in the initial conditions (ICs) are tested. It is
found that even minor changes can lead to signi cant alterations in the system. |
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