Distinguishing between folding and tearing mechanisms in strange attractors

Byrne, Greg; Gilmore, Robert; Letellier, Christophe

doi:10.1103/physreve.70.056214

Cited by 32 publications

(21 citation statements)

References 10 publications

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“…9e, f), which is supported by the Poincaré section which shows two disjoint curves (Fig. 9g) reminiscent of the Poincaré section obtained from other chaotic attractors such as the Lorenz attractor [11]. The spectral analysis, which shows a less distinctive pattern of frequencies, also supports this possibility (Fig.…”

Section: Bifurcationssupporting

confidence: 59%

Nonlinear dynamics of the CAM circadian rhythm in response to environmental forcing

Hartzell

Bartlett

Virgin

et al. 2015

Journal of Theoretical Biology

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Crassulacean acid metabolism (CAM) photosynthesis functions as an endogenous circadian rhythm coupled to external environmental forcings of energy and water availability. This paper explores the nonlinear dynamics of a new CAM photosynthesis model (Bartlett et al., 2014) and investigates the responses of CAM plant carbon assimilation to different combinations of environmental conditions. The CAM model (Bartlett et al., 2014) consists of a Calvin cycle typical of C3 plants coupled to an oscillator of the type employed in the Van der Pol and FitzHugh-Nagumo systems. This coupled system is a function of environmental variables including leaf temperature, leaf moisture potential, and irradiance. Here, we explore the qualitative response of the system and the expected carbon assimilation under constant and periodically forced environmental conditions. The model results show how the diurnal evolution of these variables entrains the CAM cycle with prevailing environmental conditions. While constant environmental conditions generate either steady-state or periodically oscillating responses in malic acid uptake and release, forcing the CAM system with periodic daily fluctuations in light exposure and leaf temperature results in quasi-periodicity and possible chaos for certain ranges of these variables. This analysis is a first step in quantifying changes in CAM plant productivity with variables such as the mean temperature, daily temperature range, irradiance, and leaf moisture potential. Results may also be used to inform model parametrization based on the observed fluctuating regime.

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Section: Bifurcationssupporting

confidence: 59%

Nonlinear dynamics of the CAM circadian rhythm in response to environmental forcing

Hartzell

Bartlett

Virgin

et al. 2015

Journal of Theoretical Biology

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“…It therefore cannot intersect the attractor. In fact, this set has the same properties as the z-axis does for the Lorenz attractor of 1963 [17]. The remaining connecting curves trace out the holes in the attractor.…”

Section: E Thomas Modelmentioning

confidence: 75%

Connecting curves for dynamical systems

Gilmore¹,

Ginoux²,

Jones³

et al. 2010

J. Phys. A: Math. Theor.

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We introduce one dimensional sets to help describe and constrain the integral curves of an n dimensional dynamical system. These curves provide more information about the system than the zero-dimensional sets (fixed points) do. In fact, these curves pass through the fixed points. Connecting curves are introduced using two different but equivalent definitions, one from dynamical systems theory, the other from differential geometry. We describe how to compute these curves and illustrate their properties by showing the connecting curves for a number of dynamical systems.

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“…where ρ A,n and ρ B,n are the ρ-coordinate of the nth intersection with the Poincaré section located in component C A and C B , respectively, and where I C is the indicator function where This was implicitly used by [Byrne et al, 2004]. Variable ρ n is thus in the range ]0; 1[∪]1; 2[.…”

Section: The Genus-3 Lorenz Attractormentioning

confidence: 99%

Toward a General Procedure for Extracting Templates from Chaotic Attractors Bounded by High Genus Torus

Rosalie

Letellier

2014

Int. J. Bifurcation Chaos

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The topological analysis of chaotic attractor by means of template is rather well established for simple attractors as solution to the Rössler system. Lorenz-like attractors are already slightly more complicated because they are bounded by a genus-3 bounding torus, implying the necessity to use a two-component Poincaré section. In this paper, we enriched the concept of linking matrix to correctly describe an algebraic template for an attractor with (g - 1) components of Poincaré section and whose bounding torus has g interior holes aligned. An example with g = 5 — a multispiral attractor — is explicitly treated.

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Distinguishing between folding and tearing mechanisms in strange attractors

Cited by 32 publications

References 10 publications

Nonlinear dynamics of the CAM circadian rhythm in response to environmental forcing

Nonlinear dynamics of the CAM circadian rhythm in response to environmental forcing

Connecting curves for dynamical systems

Toward a General Procedure for Extracting Templates from Chaotic Attractors Bounded by High Genus Torus

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