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- Title
Bifurcation and Chaos in a Fractional-Order Cournot Duopoly Game Model on Scale-Free Networks.
- Authors
Gurcan, Fuat; Kartal, Neriman; Kartal, Senol
- Abstract
In this study, a Cournot duopoly model describing Caputo fractional-order differential equations with piecewise constant arguments is discussed. We have obtained two-dimensional discrete dynamical system as a result of applying the discretization process to the model. By using the center manifold theory and the bifurcation theory, it is shown that the discrete dynamical system undergoes flip bifurcation about the Nash equilibrium point. Phase portraits, bifurcation diagrams, and Lyapunov exponents show the existence of many complex dynamical behaviors in the model such as the stable equilibrium point, period-2 orbit, period-4 orbit, period-8 orbit, period-16 orbit, and chaos according to changing the speed of the adjustment parameter v 1 . The discrete Cournot duopoly game model is also considered on two scale-free networks with different numbers of nodes. It is observed that the complex dynamical networks exhibit similar dynamical behaviors such as the stable equilibrium point, flip bifurcation, and chaos depending on changing the coupling strength parameter c s . Moreover, flip bifurcation and transition chaos take place earlier in more heterogeneous networks. Calculating the largest Lyapunov exponents guarantees the transition from nonchaotic to chaotic states in complex dynamical networks.
- Subjects
BIFURCATION diagrams; LYAPUNOV exponents; BIFURCATION theory; DYNAMICAL systems; ORBITS (Astronomy); NASH equilibrium; DIFFERENTIAL equations
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2024, Vol 34, Issue 8, p1
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127424501037