Mathematical System of Lorenz-Rössler Model: Optimal Control and Bifurcation Issues
0Mathematical System of Lorenz-Rössler Model: Optimal Control and Bifurcation Issues
Layman Abstract
This paper discusses the use of optimal control, a decision-making tool, in controlling chaotic systems, specifically the Lorenz-Rössler model, which combines two well-known models (Lorenz and Rössler). The Lorenz-Rössler system is a three-dimensional system with five parameters, and this paper focuses on understanding its behavior, including how the system can change (known as bifurcation phenomena) and how to optimally control it.
The study looks at specific conditions where the system’s behavior can change dramatically, such as the appearance of saddle-node and Hopf bifurcations. It also addresses how to determine the best control strategy to achieve the desired system behavior using a mathematical method called Pontryagin’s Maximum Principle (PMP). The paper includes numerical examples that show how these methods can be applied and how they improve our ability to control and understand chaotic systems. This research is valuable for decision-making in various fields, such as secure communications and economic systems, where understanding and controlling complex systems are important.
View Book: https://doi.org/10.9734/bpi/mcsru/v2/3835
#mathematical #lorenzomendez #bifurcation #computerscience
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