Bifurcation analysis and complex dynamics of a Kopel triopoly model

Li, Bo; Zhang, Yue; Li, Xiaoliang; Eskandari, Zohreh; He, Qizhi

doi:10.1016/j.cam.2023.115089

Cited by 48 publications

(14 citation statements)

References 39 publications

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“…Chaotic dynamical systems and bifurcation theory have many applications in applied sciences and engineering [8]. The most prominent recent research topics that should be considered are neuron models like HindMarsh-Rose [9], modeling human diseases such as cancer [10], ecological models, e.g., the famous Lotka-Volterra prey-predator model [11], chaotic fractional dynamical systems with various operators [10,12,13], and economic and financial models in game theory [14,15].…”

Section: Introductionmentioning

confidence: 99%

Coexisting attractors and multi-stability within a Lorenz model with periodic heating function

Ahmadi

Parthasarathy²,

Natiq³

et al. 2023

Phys. Scr.

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In this paper, the classical Lorenz model is under investigation, in which a periodic heating term replaces the constant one. Applying the variable heating term causes time-dependent behaviors in the Lorenz model. The time series produced by this model are chaotic; however, they have fixed point or periodic-like qualities in some time intervals. The energy dissipation and equilibrium points are examined comprehensively. This modified Lorenz system can demonstrate multiple kinds of coexisting attractors by changing its initial conditions and, thus, is a multi-stable system. Because of multi-stability, the bifurcation diagrams are plotted with three different methods, and the dynamical analysis is completed by studying the Lyapunov exponents and Kaplan-Yorke dimension diagrams. Also, the attraction basin of the modified system is investigated, which approves the appearance of coexisting attractors in this system.

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Section: Introductionmentioning

confidence: 99%

Coexisting attractors and multi-stability within a Lorenz model with periodic heating function

Ahmadi

Parthasarathy²,

Natiq³

et al. 2023

Phys. Scr.

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“…Caputo and Fabrizio further modified the Caputo operator by introducing a non-singular kernel, and in 2016, Atangana and Baleanu proposed a new definition based on Caputo’s concept using a non-local and non-singular kernel [ 21 , 22 ]. Since then, researchers have conducted considerable research on these operators, exploring various mathematical properties and applications in various fields [ 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 ].…”

Section: Introductionmentioning

confidence: 99%

Piecewise Business Bubble System under Classical and Nonsingular Kernel of Mittag–Leffler Law

Zhang

2023

Entropy

Self Cite

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This study aims to investigate the dynamics of three agents in the emerging business bubble model based on the Mittag–Leffler law pertaining to the piecewise classical derivative and non-singular kernel. By generalizing the business bubble dynamics in terms of fractional operators and the piecewise concept, this study presents a new perspective to the field. The entire set of intervals is partitioned into two piecewise intervals to analyse the classical order and conformable order derivatives of an Atangana–Baleanu operator. The subinterval analysis is critical for removing discontinuities in each sub-partition. The existence and uniqueness of the solution based on a piecewise global derivative are tested for the considered model. The approximate root of the system is determined using the piecewise numerically iterative technique of the Newton polynomial. Under the classical order and non-singular law, the approximate root scheme is applied to the piecewise derivative. The curve representation for the piece-wise globalised system is tested by applying the data for the classical and different conformable orders. This establishes the entire density of each compartment and shows a continuous spectrum instead of discrete dynamics. The concept of this study can also be applied to investigate crossover behaviours or abrupt changes in the dynamics of the values of each market.

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“…Over the past several decades, various kinds of bifurcations, such as pitchfork, trans-critical, Hopf, Neimark–Sacker (secondary Hopf), Period-doubling (flip), and/or fold (Saddle–node) bifurcations, have been proposed and analyzed [16] , [18] . Recently, numerous studies have investigated bifurcation analyses using various methods and applications, including the following models: (1) the Planar discrete-time Hindmarsh–Rose oscillator, (2) the Generalized perturbed KdV equation, (3) the Kopel model with nonsymmetric response between oligopolists, (4) the Lotka–Volterra prey–predator model, and (5) the Generalized Kopel triopoly model [19] , [20] , [21] , [22] , [23] . While future studies will apply methods for analysis of the KdV-SIR equation, this study focuses on the application of the KdV-SIR equation and its analytical solutions for COVID-19 data analysis.…”

Section: Introductionmentioning

confidence: 99%

A KdV-SIR equation and its analytical solutions: An application for COVID-19 data analysis

Paxson

Shen

2023

Chaos, Solitons & Fractals

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Bifurcation analysis and complex dynamics of a Kopel triopoly model

Cited by 48 publications

References 39 publications

Coexisting attractors and multi-stability within a Lorenz model with periodic heating function

Coexisting attractors and multi-stability within a Lorenz model with periodic heating function

Piecewise Business Bubble System under Classical and Nonsingular Kernel of Mittag–Leffler Law

A KdV-SIR equation and its analytical solutions: An application for COVID-19 data analysis

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