Hopf bifurcation of forced Chen system and its stability via adaptive control with arbitrary parameters

Marwan, Muhammad; Mehboob, Memoona; Ahmad, Salman; Aqeel, Muhammad

doi:10.1007/s00500-019-04197-8

Cited by 11 publications

(7 citation statements)

References 34 publications

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“…The specialized literature [13][14][15][16][17] has shown the importance of incorporating control theory in economic and financial analysis, highlighting its potential to enhance policy effectiveness and mitigate economic fluctuations [18,19]. Furthermore, the application of control techniques from different fields [20][21][22][23][24] has a long tradition in macroeconomics [25,26], where models incorporating feedback control [27] have been employed to address issues such as inflation control [28], and monetary policy implementation [29]. Moreover, control techniques have found utility in the study of chaotic financial systems [30,31], and in applications for risk assessment, portfolio optimization, and asset pricing, see e.g.…”

Section: Introductionmentioning

confidence: 99%

Feedback dynamic control for exiting a debt-induced spiral in a deterministic Keen model

Perez Avellaneda,

Rosales,

Duffaut Espinosa

2024

PLoS ONE

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The Keen model is designed to represent an economy as a dynamic system governed by the interactions between private debt, wage share, and employment rate. When certain conditions are met, the model can lead to a debt spiral, which accurately mimics the impact of a financial crisis on an economy. This manuscript presents a recipe for breaking this spiral by expressing Keen’s model as an affine nonlinear system that can be modified through policy interventions. We begin by considering critical initial conditions that resemble a financial crisis to achieve this goal. We then locate a desired point within the system’s vector field that leads to a desirable equilibrium and design a path towards it. This path is later followed using one-step-ahead optimal control. We illustrate our approach by presenting simulated control scenarios.

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Section: Introductionmentioning

confidence: 99%

Feedback dynamic control for exiting a debt-induced spiral in a deterministic Keen model

Perez Avellaneda,

Rosales,

Duffaut Espinosa

2024

PLoS ONE

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“…The richer and more complex behaviors under higher iterations and the bifurcation distributions of codimension-two bifurcation points are investigated [24]. In addition, various types of codimension-one and -two bifurcations have been investigated in [25][26][27][28][29][30][31][32][33] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Codimension-Two Bifurcations of a Simplified Discrete-Time SIR Model with Nonlinear Incidence and Recovery Rates

Hu,

Liu,

et al. 2023

Mathematics

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In this paper, a simplified discrete-time SIR model with nonlinear incidence and recovery rates is discussed. Here, using the integral step size and the intervention level as control parameters, we mainly discuss three types of codimension-two bifurcations (fold-flip bifurcation, 1:3 resonance, and 1:4 resonance) of the simplified discrete-time SIR model in detail by bifurcation theory and numerical continuation techniques. Parameter conditions for the occurrence of codimension-two bifurcations are obtained by constructing the corresponding approximate normal form with translation and transformation of several parameters and variables. To further confirm the accuracy of our theoretical analysis, numerical simulations such as phase portraits, bifurcation diagrams, and maximum Lyapunov exponents diagrams are provided. In particular, the coexistence of bistability states is observed by giving local attraction basins diagrams of different fixed points under different integral step sizes. It is possible to more clearly illustrate the model’s complex dynamic behavior by combining theoretical analysis and numerical simulation.

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“…A set composed of one or more than one ordinary differential equations is known as dynamical system, but the property of sensitivity to its initial conditions and parameter values gave birth to Chaos. Since 1963, uncountable work on chaos can be found such as (Rucklidge [ 12 ], Hyperjerk [ 13 ], Forced Chen [ 14 ], Transportation [ 15 ]) systems. In the beginning it was also linked with the butterfly effect.…”

Section: Introductionmentioning

confidence: 99%

Generalized external synchronization of networks based on clustered pandemic systems—The approach of Covid-19 towards influenza

Marwan,

Han,

Khan

2023

PLoS ONE

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Real-world models, like those used in social studies, epidemiology, energy transport, engineering, and finance, are often called “multi-layer networks.” In this work, we have described a controller that connects the paths of synchronized models that are grouped together in clusters. We did this using Lyapunov theory and a variety of coupled matrices to look into the link between the groups of chaotic systems based on influenza and covid-19. Our work also includes the use of external synchrony in biological systems. For example, we have explained in detail how the pandemic disease covid-19 will get weaker over time and become more like influenza. The analytical way to get these answers is to prove a theorem, and the numerical way is to use MATLAB to run numerical simulations.

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Hopf bifurcation of forced Chen system and its stability via adaptive control with arbitrary parameters

Cited by 11 publications

References 34 publications

Feedback dynamic control for exiting a debt-induced spiral in a deterministic Keen model

Feedback dynamic control for exiting a debt-induced spiral in a deterministic Keen model

Codimension-Two Bifurcations of a Simplified Discrete-Time SIR Model with Nonlinear Incidence and Recovery Rates

Generalized external synchronization of networks based on clustered pandemic systems—The approach of Covid-19 towards influenza

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