A canonical model of multistability and scale-invariance in biological systems.

Multistability and scale-invariant fluctuations occur in a wide variety of biological organisms from bacteria to humans as well as financial, chemical and complex physical systems. Multistability refers to noise driven switches between multiple weakly stable states. Scale-invariant fluctuations aris...

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Main Authors: Frank Freyer, James A Roberts, Petra Ritter, Michael Breakspear
Format: Article
Language:English
Published: Public Library of Science (PLoS) 2012-01-01
Series:PLoS Computational Biology
Online Access:https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1002634&type=printable
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author Frank Freyer
James A Roberts
Petra Ritter
Michael Breakspear
author_facet Frank Freyer
James A Roberts
Petra Ritter
Michael Breakspear
author_sort Frank Freyer
collection DOAJ
description Multistability and scale-invariant fluctuations occur in a wide variety of biological organisms from bacteria to humans as well as financial, chemical and complex physical systems. Multistability refers to noise driven switches between multiple weakly stable states. Scale-invariant fluctuations arise when there is an approximately constant ratio between the mean and standard deviation of a system's fluctuations. Both are an important property of human perception, movement, decision making and computation and they occur together in the human alpha rhythm, imparting it with complex dynamical behavior. Here, we elucidate their fundamental dynamical mechanisms in a canonical model of nonlinear bifurcations under stochastic fluctuations. We find that the co-occurrence of multistability and scale-invariant fluctuations mandates two important dynamical properties: Multistability arises in the presence of a subcritical Hopf bifurcation, which generates co-existing attractors, whilst the introduction of multiplicative (state-dependent) noise ensures that as the system jumps between these attractors, fluctuations remain in constant proportion to their mean and their temporal statistics become long-tailed. The simple algebraic construction of this model affords a systematic analysis of the contribution of stochastic and nonlinear processes to cortical rhythms, complementing a recently proposed biophysical model. Similar dynamics also occur in a kinetic model of gene regulation, suggesting universality across a broad class of biological phenomena.
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spelling doaj-art-ca050eba9f54429e808dd16de4f595dc2025-08-20T03:11:57ZengPublic Library of Science (PLoS)PLoS Computational Biology1553-734X1553-73582012-01-0188e100263410.1371/journal.pcbi.1002634A canonical model of multistability and scale-invariance in biological systems.Frank FreyerJames A RobertsPetra RitterMichael BreakspearMultistability and scale-invariant fluctuations occur in a wide variety of biological organisms from bacteria to humans as well as financial, chemical and complex physical systems. Multistability refers to noise driven switches between multiple weakly stable states. Scale-invariant fluctuations arise when there is an approximately constant ratio between the mean and standard deviation of a system's fluctuations. Both are an important property of human perception, movement, decision making and computation and they occur together in the human alpha rhythm, imparting it with complex dynamical behavior. Here, we elucidate their fundamental dynamical mechanisms in a canonical model of nonlinear bifurcations under stochastic fluctuations. We find that the co-occurrence of multistability and scale-invariant fluctuations mandates two important dynamical properties: Multistability arises in the presence of a subcritical Hopf bifurcation, which generates co-existing attractors, whilst the introduction of multiplicative (state-dependent) noise ensures that as the system jumps between these attractors, fluctuations remain in constant proportion to their mean and their temporal statistics become long-tailed. The simple algebraic construction of this model affords a systematic analysis of the contribution of stochastic and nonlinear processes to cortical rhythms, complementing a recently proposed biophysical model. Similar dynamics also occur in a kinetic model of gene regulation, suggesting universality across a broad class of biological phenomena.https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1002634&type=printable
spellingShingle Frank Freyer
James A Roberts
Petra Ritter
Michael Breakspear
A canonical model of multistability and scale-invariance in biological systems.
PLoS Computational Biology
title A canonical model of multistability and scale-invariance in biological systems.
title_full A canonical model of multistability and scale-invariance in biological systems.
title_fullStr A canonical model of multistability and scale-invariance in biological systems.
title_full_unstemmed A canonical model of multistability and scale-invariance in biological systems.
title_short A canonical model of multistability and scale-invariance in biological systems.
title_sort canonical model of multistability and scale invariance in biological systems
url https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1002634&type=printable
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