Multiple and generic bifurcation analysis of a discrete Hindmarsh-Rose model

Li, Bo; Liang, Houjun; He, Qizhi

doi:10.1016/j.chaos.2021.110856

Cited by 78 publications

(19 citation statements)

References 32 publications

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“…Useful information about the past and present of the disease has been reported, which is advantageous in establishing control strategies for its eradication from society. In this regard, valuable work can be found in [11,12,13,14,15,16]. The formation of a mathematical formula consists of conditions regarding the parameters involved in the problem under consideration.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a fractional-order COVID-19 model under the nonsingular kernel of Caputo-Fabrizio operator

Ahmad

Qiu

Rahman

2022

mmnsa

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For the sake of human health, it is crucial to investigate infectious diseases including HIV/AIDS, hepatitis, and others. Worldwide, the recently discovered new coronavirus (COVID-19) poses a serious threat. The experimental vaccination and different COVID-19 strains found around the world make the virus' spread unavoidable. In the current research, fractional order is used to study the dynamics of a nonlinear modified COVID-19 SEIR model in the framework of the Caputo-Fabrizio fractional operator with order b. Fixed point theory has been used to investigate the qualitative analysis of the solution respectively. The well-known Laplace transform method is used to determine the approximate solution of the proposed model. Using the COVID-19 data that is currently available, numerical simulations are run to validate the necessary scheme and examine the dynamic behavior of the various compartments of the model. In order to stop the pandemic from spreading, our findings highlight the significance of taking preventative steps and changing one's lifestyle.

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Section: Introductionmentioning

confidence: 99%

Dynamics of a fractional-order COVID-19 model under the nonsingular kernel of Caputo-Fabrizio operator

Ahmad

Qiu

Rahman

2022

mmnsa

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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

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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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“…The appearance of the Hopf bifurcation represents the basic beginning of the quasi-periodic path to chaos, when the spiral node becomes unstable, and passes into the limit cycle through the Hopf bifurcation, after which chaos appears. The study of bifurcation can be found in papers [1]- [4], in addition to bifurcations associated with continuous systems, this phenomenon also occurs in discrete systems, where the common name is Neimark-Sacker bifurcation, an example of such bifurcations is in papers [5]- [7].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we use the theory developed in paper [8], [9], [10], and [11]. The study and significance of the ordinary differential equation (ODE) system were in the works [12]- [17] and the discrete system was in the works [5]- [7].…”

Section: Introductionmentioning

confidence: 99%

Dynamics and Bifurcation for One Non-linear System

et al. 2023

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In this paper, we observed the ordinary differential equation (ODE) system and determined the equilibrium points. To characterize them, we used the existing theory developed to visualize the behavior of the system. We describe the bifurcation that appears, which is characteristic of higher-dimensional systems, that is when a fixed point loses its stability without colliding with other points. Although it is difficult to determine the whole series of bifurcations that lead to chaos, we can say that it is a common opinion that it is precisely the Hopf bifurcation that leads to chaos when it comes to situations that occur in applications. Here, subcritical and supercritical bifurcation occurs, and we can say that subcritical bifurcation represents a much more dramatic situation and is potentially more dangerous than supercritical bifurcation, technically speaking. Namely, bifurcations or trajectories jump to a distant attractor, which can be a fixed point, limit cycle, infinity, or in spaces with three or more dimensions, a foreign attractor.

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Multiple and generic bifurcation analysis of a discrete Hindmarsh-Rose model

Cited by 78 publications

References 32 publications

Dynamics of a fractional-order COVID-19 model under the nonsingular kernel of Caputo-Fabrizio operator

Dynamics of a fractional-order COVID-19 model under the nonsingular kernel of Caputo-Fabrizio operator

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

Dynamics and Bifurcation for One Non-linear System

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