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Stability analysis of distributed order fractional chen system
H Aminikhah1, A Refahi Sheikhani2, H Rezazadeh1
1Department of Applied Mathematics, School of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran.
Thescientificworldjournal
|February 4, 2014
Summary
This study establishes stability conditions for nonlinear distributed order fractional systems. Researchers found chaos in the double fractional order Chen system, verifying results with numerical solutions.
Area of Science:
- Nonlinear dynamics
- Fractional calculus
- Chaos theory
Background:
- Nonlinear distributed order fractional systems are complex dynamical systems.
- The integer-order Chen system is a well-known chaotic system.
- Understanding stability and dynamics in fractional domains is crucial for advanced modeling.
Purpose of the Study:
- To investigate the stability conditions for nonlinear distributed order fractional systems.
- To generalize the integer-order Chen system to the distributed order fractional domain.
- To analyze the stability and identify chaotic behaviors in the fractional-order Chen system.
Main Methods:
- Derivation of sufficient and necessary conditions for system stability.
- Generalization of the Chen system into a distributed order fractional model.
- Application of asymptotic stability theory for nonlinear distributed order fractional systems.
- Numerical simulations to validate analytical findings.
Main Results:
- Sufficient and necessary conditions for the stability of nonlinear distributed order fractional systems were established.
- The distributed order fractional Chen system was successfully formulated.
- Chaos was identified in the double fractional order Chen system.
- Numerical solutions confirmed the analytical predictions regarding system stability and chaos.
Conclusions:
- The study provides a theoretical framework for analyzing the stability of nonlinear distributed order fractional systems.
- The generalized fractional-order Chen system exhibits complex dynamics, including chaos.
- Numerical verification supports the theoretical findings, highlighting the potential for rich dynamics in fractional systems.
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