Intrinsic stochasticity can induce highly non-trivial effects on dynamical systems, such as stochastic resonance, noise induced bistability, and noise-induced oscillations, to name but a few. Here we revisit a mechanism - first investigated in the context of neuroscience - by which relatively small intrinsic (demographic) fluctuations can lead to the emergence of avalanching behavior in systems that are deterministically characterized by a single stable fixed point (up state). The anomalously large response of such systems to stochasticity stems from (or is strongly associated with) the existence of a 'non-normal' stability matrix at the deterministic fixed point, which may induce the system to be 'reactive'. By employing a number of analytical and computational approaches, we further investigate this mechanism and explore the interplay between non-normality and intrinsic stochasticity. In particular, we conclude that the resulting dynamics of this type of systems cannot be simply derived from a scalar potential but, additionally, one needs to consider a curl flux which describes the essential non-equilibrium nature of this type of noisy non-normal systems. Moreover, we shed further light on the origin of the phenomenon, introduce the novel concept of 'non-linear reactivity', and rationalize the observed values of avalanche exponents.

Non-normality, reactivity, and intrinsic stochasticity in neural dynamics: A non-equilibrium potential approach / Di Santo, Serena; Villegas, Pablo; Burioni, Raffaella; Muñoz, Miguel A.. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2018:7(2018), pp. 073402-073425. [10.1088/1742-5468/aacda3]

Non-normality, reactivity, and intrinsic stochasticity in neural dynamics: A non-equilibrium potential approach

Di Santo, Serena;Burioni, Raffaella;Muñoz, Miguel A.
2018

Abstract

Intrinsic stochasticity can induce highly non-trivial effects on dynamical systems, such as stochastic resonance, noise induced bistability, and noise-induced oscillations, to name but a few. Here we revisit a mechanism - first investigated in the context of neuroscience - by which relatively small intrinsic (demographic) fluctuations can lead to the emergence of avalanching behavior in systems that are deterministically characterized by a single stable fixed point (up state). The anomalously large response of such systems to stochasticity stems from (or is strongly associated with) the existence of a 'non-normal' stability matrix at the deterministic fixed point, which may induce the system to be 'reactive'. By employing a number of analytical and computational approaches, we further investigate this mechanism and explore the interplay between non-normality and intrinsic stochasticity. In particular, we conclude that the resulting dynamics of this type of systems cannot be simply derived from a scalar potential but, additionally, one needs to consider a curl flux which describes the essential non-equilibrium nature of this type of noisy non-normal systems. Moreover, we shed further light on the origin of the phenomenon, introduce the novel concept of 'non-linear reactivity', and rationalize the observed values of avalanche exponents.
Non-normality, reactivity, and intrinsic stochasticity in neural dynamics: A non-equilibrium potential approach / Di Santo, Serena; Villegas, Pablo; Burioni, Raffaella; Muñoz, Miguel A.. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2018:7(2018), pp. 073402-073425. [10.1088/1742-5468/aacda3]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2849782
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