Hopf bifurcation, offset boosting and remerging Feigenbaum trees in an autonomous chaotic system with exponential nonlinearity

Wouapi, K. Marcel; Fotsin, B. Hilaire; Feudjio, K. Florent; Njitacke, Zeric Tabekoueng

doi:10.1007/s42452-019-1702-y

Cited by 17 publications

(2 citation statements)

References 61 publications

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“…5C and E). A reverse perioddoubling bifurcation (antimonotonicity) in ⟨ v r ⟩ is observed (Dawson et al, 1992; Wouapi et al, 2019). In both cases the bifurcation is less prominent, as it only ranges for about Δ R = 2 μm and shows minor variations in ⟨ v r ⟩ .…”

Section: Resultsmentioning

confidence: 96%

Self-organization of PIP3 signaling is controlled by the confinement, topology, and curvature of the cell membrane

Erisis,

Hörning

2024

Preprint

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PIP3 is a signaling lipid on the plasma membrane that plays a fundamental role in cell signaling with a strong impact on cell physiology and diseases. It is responsible for the protruding edge formation, cell polarization, macropinocytosis and other membrane remodeling dynamics in cells. It has been shown that the membrane confinement and curvature affects the wave formation of PIP3 and F-actin. But even in the absence of F-actin, a complex self-organization of the spatiotemporal PIP3 waves is observed. In recent findings, we have shown that these waves can be guided and pinned on strongly bended Dictyostelium membranes caused by molecular crowding and curvature limited diffusion. Based on these experimental findings, we investigate the spatiotemporal PIP3 wave dynamics on realist 3D cell-like membranes to explore the effect of curvature limited diffusion, as observed experimentally. We use an established stochastic reaction-diffusion model with enzymatic Michaelis-Menten type reactions that mimics the dynamics of Dictyostelium cells. As these cells mimic the 3D shape and size observed experimentally, we found that the PIP3 wave directionality can be explained by a Hopf-like and a reverse periodic-doubling bifurcation for uniform diffusion and curvature limited diffusion properties. Finally, we compare the results with recent experimental findings and discuss the discrepancy between the biological and numerical results.

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Section: Resultsmentioning

confidence: 96%

Self-organization of PIP3 signaling is controlled by the confinement, topology, and curvature of the cell membrane

Erisis,

Hörning

2024

Preprint

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“…This is the case of the Van der Pol (VdP) biological model, van der Pol-Duffing [43,44], the hyperjeck system [44], memristive Jerk system [45] and many others. The antimonotonicity in the model is characterized by a periodic zone on either side and separated by irregular, chaotic envelopes that remain symmetrical for the chosen conditions [46]; figure 15…”

Section: Reemerging Feigenbaum and Anti-monotonicitymentioning

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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Dimensionality reduction of chaos by feedbacks and periodic forcing is a source of natural climate change

Salmon

2024

Clim Dyn

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Hopf bifurcation, offset boosting and remerging Feigenbaum trees in an autonomous chaotic system with exponential nonlinearity

Abstract: The present paper executes an analysis of a relatively simple chaotic system with exponential nonlinearity. This dimensionless dynamic system has been obtained from the chaotic circuit introduced by Ma and collaborators (nonlinear Dyn.

Cited by 17 publications

References 61 publications

Self-organization of PIP3 signaling is controlled by the confinement, topology, and curvature of the cell membrane

Self-organization of PIP3 signaling is controlled by the confinement, topology, and curvature of the cell membrane

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

Dimensionality reduction of chaos by feedbacks and periodic forcing is a source of natural climate change

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