Bifurcations in a birhythmic biological system with time-delayed noise

Chamgoué, André Chéagé; Yamapi, R.; Woafo, P.

doi:10.1007/s11071-013-0931-7

Cited by 38 publications

(5 citation statements)

References 19 publications

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“…How to derive the stationary probability density for stochastic multi‐species chemostat model is a challenging problem. Another interesting problem is investigating the effect of time delay 33–35 on the stationary probability density for stochastic chemostat model. These problems deserve further investigation.…”

Section: Simulation and Discussionmentioning

confidence: 99%

Stationary probability density of a stochastic chemostat model with Monod growth response function

2021

Math Methods in App Sciences

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The stationary probability density (SPD) is derived and studied for a stochastic chemostat model with Monod growth response function. First, with the help of polar coordinate transformation and stochastic averaging method, we derive a two-dimensional diffusion process of averaged amplitude and phase angle. Furthermore, the SPD of the diffusion process is obtained by the corresponding Fokker Planck-Kolmogorov equation. We also analyze the effects of noise intensities on the geometric property of the SPD.

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Section: Simulation and Discussionmentioning

confidence: 99%

Stationary probability density of a stochastic chemostat model with Monod growth response function

2021

Math Methods in App Sciences

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“…Enzyme substrate assembly and protein-protein binding constitute a metabolic pathway for formation and rupture that responds dynamically to biochemical stimulus conditions. The effects of electromagnetic flux have been taken into account by introducing transformations in the neural models [33][34][35]. In heart cells [36,37], neural networks coupled to magnetic flux have also been studied in [38,39] allowing the identification of various spatiotemporal patterns including wave propagation and chimeric states.…”

Section: The Self-sustained Biological Model Coupled To a Magnetic Fluxmentioning

confidence: 99%

“…A Hopf bifurcation typically causes the appearance (or disappearance) of a limit cycle around the equilibrium points. Hopf bifurcation is of great importance in the digestion of foodstuffs that we consume daily [34,36]. It should be noted that the origin of the Hopf point here represents the beginning of the reaction of salivary amylase (an enzyme that hydrolyzes cooked starch (the main component of starchy foods) to generate glucose, maltose, and dextrins) on cooked starch (substrate).…”

Section: Hopf Bifurcation Origin and Stabilitymentioning

confidence: 99%

Influence of the magnetic flux on the dynamics of a self-sustaining system: analytical, numerical and analogical investigations

Dang-Ra,

Chéagé Chamgoué,

Wouapi

et al. 2024

Phys. Scr.

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This paper investigates the nonlinear dynamics of a ferroelectric enzyme-substratereaction modeled by \textcolor{red}{the} bi-rhythmic \emph{van der Pol} oscillator coupled to \textcolor{red}{the} magneticflux. We derive the equilibrium points and study their stability.We analyze some bifurcation structures and the variation of the Lyapunov exponents.The phenomena of symmetric attractors and the anti-monotonicity are observed. \textcolor{red}{By} increasing the magnetic flux, \textcolor{red}{we find that the equilibrium points are stable}, tends to control chaotic regimes, and affects regular and quasi-regular ones. As the magnetic flux increases, the amplitude of the oscillations around the equilibrium points decreases and the \textcolor{red}{amplitude of the} limit cycles at the Hopf bifurcation \textcolor{red}{tends} to disappear. Further \textcolor{red}{increasing the magnetic flux gives} rise to chaotic dynamics. The electrical circuit and analogical simulations are \textcolor{red}{derived} using the PSpice software.\textcolor{red}{The agreement between analogical and numerical results is acceptable}.

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“…The working mechanism of an enzymatic reaction can be aected by the inuence of electromagnetic fields that form in the vicinity of enzymes. The eects of electromagnetic flux have been taken into account by introducing transformations in the neural models [25][26][27]. In heart cells [28,29], neural networks coupled to magnetic ux have also been studied in refs.…”

Section: A the Self-sustained Biological Model Without Magnetic Induc...mentioning

confidence: 99%

“…Hopf bifurcation is of great importance in the digestion of foodstuffs that we consume daily [26,28]. It should be noted that the origin of the Hopf point here represents the beginning of the reaction of salivary amylase (an enzyme that hydrolyzes cooked starch (the main component of starchy foods) to generate glucose, maltose, and dextrins) on cooked starch (substrate).…”

Section: B Stability Of Equilibrium Pointsmentioning

confidence: 99%

Influence of the Magnetic Flux on the Dynamics of a self-sustained System: Analytical, numerical and analogical investigations

DANG-RA,

chamgoue,

WOUAPI

et al. 2023

Preprint

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This paper investigates the nonlinear dynamics of a ferroelectric enzyme-substrate reaction modeled by a bi-rhythmic Van der Pol oscillator coupled to a magnetic flux. We derive the equilibrium points and study their stability, analyze some bifurcation structures and the variation of the corresponding Lyapunov exponents. The phenomena of symmetric attractors and the anti-monotonicity are observed. An increasing the magnetic ﬂux stabilizes the equilibrium points, tends to control chaotic regimes, and aﬀect regular and quasi-regular ones. As the magnetic ﬂux increases, the amplitude of oscillations around the equilibrium point decreases and the limit cycles at the hopf bifurcation tend to disappear. Further increases the magnetic flux giving rise to chaotic dynamics. The electrical circuit and analogical simulations are performed using PSpice software. Analogical and numerical results agree.

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Bifurcations in a birhythmic biological system with time-delayed noise

Cited by 38 publications

References 19 publications

Stationary probability density of a stochastic chemostat model with Monod growth response function

Stationary probability density of a stochastic chemostat model with Monod growth response function

Influence of the magnetic flux on the dynamics of a self-sustaining system: analytical, numerical and analogical investigations

Influence of the Magnetic Flux on the Dynamics of a self-sustained System: Analytical, numerical and analogical investigations

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