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Article

Complex Dynamic Analysis for a Rent-Seeking Game with Political Competition and Policymaker Costs

by
Xiuqin Yang
1,*,
Feng Liu
2,3,4,* and
Hua Wang
5
1
School of Education, Minzu University, Beijing 100081, China
2
School of Automation, China University of Geosciences, Wuhan 430074, China
3
Engineering Research Center of Ministry of Education for Intelligent Technology of Earth Exploration, Wuhan 430074, China
4
Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan 430074, China
5
Department of Mechanical Engineering, Boston University, Boston, MA 02215, USA
*
Authors to whom correspondence should be addressed.
Mathematics 2023, 11(21), 4524; https://doi.org/10.3390/math11214524
Submission received: 26 September 2023 / Revised: 27 October 2023 / Accepted: 1 November 2023 / Published: 2 November 2023
(This article belongs to the Special Issue Mathematical Methods for Nonlinear Dynamics)
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Abstract

This paper investigates the dynamics of rent-seeking games that include political competition and policymaker cost model. The local asymptotic stability of multiple equilibrium points and Nash equilibrium points are studied. In the rent-seeking model, the existence and stability of Flip bifurcation and Neimark–Sacker bifurcation are examined, and the corresponding theorems and conditions are derived. The theoretical conclusions of the paper are verified by numerical simulations with different parameters. The simulation graphics show that the rent-seeking game model exhibits rich dynamic behaviors, such as multi-periodic orbits, Flip bifurcation, Neimark–Sacker bifurcation, and chaotic sets.
Keywords: stability; rent-seeking games; flip bifurcation; Neimark–Sacker bifurcation stability; rent-seeking games; flip bifurcation; Neimark–Sacker bifurcation

Share and Cite

MDPI and ACS Style

Yang, X.; Liu, F.; Wang, H. Complex Dynamic Analysis for a Rent-Seeking Game with Political Competition and Policymaker Costs. Mathematics 2023, 11, 4524. https://doi.org/10.3390/math11214524

AMA Style

Yang X, Liu F, Wang H. Complex Dynamic Analysis for a Rent-Seeking Game with Political Competition and Policymaker Costs. Mathematics. 2023; 11(21):4524. https://doi.org/10.3390/math11214524

Chicago/Turabian Style

Yang, Xiuqin, Feng Liu, and Hua Wang. 2023. "Complex Dynamic Analysis for a Rent-Seeking Game with Political Competition and Policymaker Costs" Mathematics 11, no. 21: 4524. https://doi.org/10.3390/math11214524

APA Style

Yang, X., Liu, F., & Wang, H. (2023). Complex Dynamic Analysis for a Rent-Seeking Game with Political Competition and Policymaker Costs. Mathematics, 11(21), 4524. https://doi.org/10.3390/math11214524

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