New insight into bifurcation of fractional-order 4D neural networks incorporating two different time delays

Xu, Changjin; Mu, Dan; Liu, Zixin; Pang, Yicheng; Liao, Maoxin; Aouiti, Chaouki

doi:10.1016/j.cnsns.2022.107043

Cited by 80 publications

(36 citation statements)

References 49 publications

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“…The qualitative behavior is explored for proposed model and our investigation proves the consistency preserving properties. Taking into account the fact that the fractional-order chemical reaction systems have the potential to improve our understanding of a wide range of chemical processes and to provide new insights into the behavior and control of these systems [29][30][31][32][33][34], we will consider a fractional-order counterpart of the system (3) for our future investigation.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Stability, Discretization, and Bifurcation Analysis for a Chemical Reaction System

Din¹,

Saeed²

2023

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Chemical reactions reveal all types of exotic behavior, that is, multistability, oscillation, chaos, or multistationarity. The mathematical framework of rate equations enables us to discuss steadystates, stability and oscillatory behavior of a chemical reaction. A planar cubic dynamical system governed by nonlinear differential equations induced by kinetic differential equations for a two-species chemical reaction is studied. It is investigated that system has unique positive steady state. Moreover, local dynamics of system is studied around its positive steady state. Existence and direction of Hopf bifurcation about positive equilibrium are carried out. In order to modify the bifurcating behavior, bifurcation control is investigated. Keeping in mind, a consistency preserving discretization for continuous chemical reaction system, a discrete counterpart is proposed, and its qualitative behavior is investigated. Numerical simulation along with bifurcation diagrams are provided to illustrate the mathematical investigations.

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Section: Numerical Simulationsmentioning

confidence: 99%

Stability, Discretization, and Bifurcation Analysis for a Chemical Reaction System

Din¹,

Saeed²

2023

match

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“…Tus, the smaller the fractional-order, the more drastic the instability of the function becomes. Tis assertion will be further investigated in comparison with other models [17] in future research, where the bifurcation properties of the fractional-order delay diferential cobweb model will be discussed as shown in the related articles [17][18][19][20][21] and then assessed for the practical implication of the bifurcation of price in the market.…”

Section: Numerical Solutionmentioning

confidence: 99%

Price Dynamics of a Delay Differential Cobweb Model

Anokye

Barnes

Boateng³

et al. 2023

Discrete Dynamics in Nature and Society

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The paper uses a new technique to find a unique solution to a delay differential cobweb model (formulated from a joint supply-demand function of price) with real model parameters via the Lambert W-function without considering any complex branches. The dynamics of the model are demonstrated with simulations and found to complement previous studies using literature values. However, the condition for instability δ / β > 1 in the previous studies was defied by our model due to the time delay associated with the supply function. The practical application and advantage of this model over the existing models are that the stability of this model is not limited to only the ratio of price elasticity of demand and supply but also the time-delay parameter (i.e., a missing link in the previous models). Our model, on the other hand, loses its stability when the time delay associated with the supply function is fixed at τ = 1.8 . Since most of the physical systems, including economical systems, are time-delay inherent and such stability conditionalities should not limit their performance, it is recommended that such systems be modelled using delay differential functions. The novelty of this research is that there has not been a definite general solution to the cobweb model with a time delay whose price dynamics mimic the behaviour of the existing cobweb models in the literature. An illustrative example in a delayed fractional-order differential equation also buttressed the importance of the time delay in the model, aside from the impact of the ratio of the price elasticity of supply and demand.

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“…Eshaghi et al [29] discussed the bifurcation, synchronization, and chaos control of a fractional-order chaotic system. For more details, one can see [29,[34][35][36][37][38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Exploring Dynamics and Hopf Bifurcation of a Fractional-Order Bertrand Duopoly Game Model Incorporating Both Nonidentical Time Delays

et al. 2023

Fractal Fract

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In order to maximize benefits, oligopolistic competition often occurs in contemporary society. Establishing the mathematical models to reveal the law of market competition has become a vital topic. In the current study, on the basis of the earlier publications, we propose a new fractional-order Bertrand duopoly game model incorporating both nonidentical time delays. The dynamics involving existence and uniqueness, non-negativeness, and boundedness of solution to the considered fractional-order Bertrand duopoly game model are systematacially analyzed via the Banach fixed point theorem, mathematical analysis technique, and construction of an appropriate function. Making use of different delays as bifurcation parameters, several sets of new stability and bifurcation conditions ensuring the stability and the creation of Hopf bifurcation of the established fractional-order Bertrand duopoly game model are acquired. By virtue of a proper definite function, we set up a new sufficient condition that ensures globally asymptotically stability of the considered fractional-order Bertrand duopoly game model. The work reveals the impact of different types of delays on the stability and Hopf bifurcation of the proposed fractional-order Bertrand duopoly game model. The study shows that we can adjust the delay to achieve price balance of different products. To confirm the validity of the derived criteria, we put computer simulation into effect. The derived conclusions in this article are wholly new and have great theoretical value in administering companies.

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New insight into bifurcation of fractional-order 4D neural networks incorporating two different time delays

Cited by 80 publications

References 49 publications

Stability, Discretization, and Bifurcation Analysis for a Chemical Reaction System

Stability, Discretization, and Bifurcation Analysis for a Chemical Reaction System

Price Dynamics of a Delay Differential Cobweb Model

Exploring Dynamics and Hopf Bifurcation of a Fractional-Order Bertrand Duopoly Game Model Incorporating Both Nonidentical Time Delays

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