Chaos Control and Anti-Control of the Heterogeneous Cournot Oligopoly Model

Abstract

The main aim of this paper focuses on chaos suppression (control) and stimulation (anti-control) of a heterogeneous Cournot oligopoly model. This goal is reached by applying the theory of dynamical systems, namely impulsive control. The main aim was to demonstrate, through massive numerical simulations and estimation of the maximal Lyapunov exponent, the 0-1test for chaos, and bifurcation analysis, that it is possible to control the dynamical behavior of the investigated model by finding injection values under which the desired phenomena are attained. Moreover, it was shown that there are injection values for which the injected system admits a self-excited cycle or chaotic trajectory.

On risk and market sentiments driving financial share price dynamics

“…Bielawski et al [28] studied the emergence of chaotic behaviour of Follow-the-Regularised Leader (FoReL) dynamics in games and found that an increase in the population size or the scale of costs in congestion games results in unstable chaotic behaviours. Furthermore, similarly to Lampart and Lampartová [29] and Lampart et al [24], Bielawski et al [28] demonstrate the coexistence of stable Nash equilibria and chaos where the creation of one chaotic attractor is simultaneous with the destruction of another. Elsadany and Awad [30] describe the behaviour of a duopolistic Bertrand competitive market with environmental taxes where representative agents are privatised or non-privatised public firms.…”

“…(see, e.g. [29]). Impulse control is only applied once in our case, in a consecutive finite number of iterations, reflecting the nature of the researched problem.…”

Chaos Generation With Impulse Control: Application to Non-Chaotic Systems and Circuit Design

“…A feedback chaos anti-control method for discrete systems was proposed by Lai and Chen [24]. Impulse control is applied to the discrete system, named heterogeneous cournot oligopoly model, for chaos generation through constant impulse signal [27]. Chaos generation from discrete system in the sense of Li-Yorke [24], [25], [28]- [31] was simpler than that from continuous time system, because, the dynamical analysis in continuous time system is more difficult.…”