Zobrazeno 1 - 10
of 70
pro vyhledávání: '"TOUBOUL, JONATHAN D."'
We analyze a spatially extended version of a well-known model of forest-savanna dynamics, which presents as a system of nonlinear partial integro-differential equations, and study necessary conditions for pattern-forming bifurcations. Analytically, w
Externí odkaz:
http://arxiv.org/abs/2308.13438
Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described by nonlin
Externí odkaz:
http://arxiv.org/abs/2305.05007
A variety of nonlinear models of biological systems generate complex chaotic behaviors that contrast with biological homeostasis, the observation that many biological systems prove remarkably robust in the face of changing external or internal condit
Externí odkaz:
http://arxiv.org/abs/2209.05638
Experimental characterization of neuronal dynamics involves recording both of spontaneous activity patterns and of responses to transient and sustained inputs. While much theoretical attention has been devoted to the spontaneous activity of neurons,
Externí odkaz:
http://arxiv.org/abs/2007.11968
Autor:
Destexhe, Alain, Touboul, Jonathan D.
Many studies have found evidence that the brain operates at a critical point, a processus known as self-organized criticality. A recent paper found remarkable scalings suggestive of criticality in systems as different as neural cultures, anesthetized
Externí odkaz:
http://arxiv.org/abs/2002.08813
Publikováno v:
SIAM Journal on Applied Dynamical Systems, 2020, 19(4): 2682-2719
Deterministic models of vegetation often summarize, at a macroscopic scale, a multitude of intrinsically random events occurring at a microscopic scale. We bridge the gap between these scales by demonstrating convergence to a mean-field limit for a g
Externí odkaz:
http://arxiv.org/abs/1911.06770
Publikováno v:
Phys. Rev. X 10, 011073 (2020)
We study the statistical physics of a surprising phenomenon arising in large networks of excitable elements in response to noise: while at low noise, solutions remain in the vicinity of the resting state and large-noise solutions show asynchronous ac
Externí odkaz:
http://arxiv.org/abs/1905.01342
We investigate the dynamics of a limit of interacting FitzHugh-Nagumo neurons in the regime of large interaction coefficients. We consider the dynamics described by a mean-field model given by a nonlinear evolution partial differential equation repre
Externí odkaz:
http://arxiv.org/abs/1804.06758
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In a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents mathematical analysis
Externí odkaz:
http://arxiv.org/abs/1611.02740