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12 November 2024 Study on the complex dynamics and chaos control for Bertrand duopoly game models with emission charges
Yvfang Feng, Linjing Lu, Yehaolin Ling
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Proceedings Volume 13395, International Conference on Optics, Electronics, and Communication Engineering (OECE 2024) ; 133952C (2024) https://doi.org/10.1117/12.3048993
Event: International Conference on Optics, Electronics, and Communication Engineering, 2024, Wuhan, China
Abstract
In this paper we consider a nonlinear Bertrand game model and investigate the dynamical properties. It is assumed that the two competitors follow linear cost functions and quadratic emission charges. We construct a two-dimensional system for the model first. Then we examine the equilibrium points and their stability conditions. The chaotic properties are presented numerically via bifurcation diagrams, maximum Lyapunov exponent, sensitive dependence on initial conditions and strange attractors. Finally, we control the chaotic behavior by time-delay feedback method.
(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.
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Yvfang Feng, Linjing Lu, and Yehaolin Ling "Study on the complex dynamics and chaos control for Bertrand duopoly game models with emission charges", Proc. SPIE 13395, International Conference on Optics, Electronics, and Communication Engineering (OECE 2024) , 133952C (12 November 2024); https://doi.org/10.1117/12.3048993
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KEYWORDS
Chaos
Control systems
Pollution
Dynamical systems
Feedback control
Mathematical modeling
Matrices
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