Dynamical Principles of Emotion-Cognition Interaction: Mathematical Images of Mental Disorders

Rabinovich, M. I.; Muezzinoglu, Mehmet K.; Strigo, Irina A.; Bystritsky, Alexander

doi:10.1371/journal.pone.0012547

Cited by 47 publications

(46 citation statements)

References 79 publications

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“…It has also been shown that metastable states play a key role in the execution of cognitive functions. Indeed, experimental and modeling studies suggest that most of these functions are the result of transient activity of large-scale brain networks in the presence of noise [38,39]. In our case the spontaneous activity represented by the heteroclinic network corresponds to switches between multiple states where each state is a specific textural feature.…”

Section: Resultsmentioning

confidence: 76%

Bifurcation Diagrams and Heteroclinic Networks of Octagonal H-Planforms

Faye

Chossat

2012

J Nonlinear Sci

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This paper completes the classification of bifurcation diagrams for H-planforms in the Poincaré disc D whose fundamental domain is a regular octagon. An H-planform is a steady solution of a PDE or integro-differential equation in D, which is invariant under the action of a lattice subgroup Γ of U (1, 1), the group of isometries of D. In our case Γ generates a tiling of D with regular octagons. This problem was introduced as an example of spontaneous pattern formation in a model of image feature detection by the visual cortex where the features are assumed to be represented in the space of structure tensors. Under "generic" assumptions the bifurcation problem reduces to an ODE which is invariant by an irreducible representation of the group of automorphisms G of the compact Riemann surface D/Γ. The irreducible representations of G have dimension one, two, three and four. The bifurcation diagrams for the representations of dimension less than four have already been described and correspond to already well known goup actions. In the present work we compute the bifurcation diagrams for the remaining three irreducible representations of dimension four, thus completing the classification. In one of these cases, there is generic bifurcation of a heteroclinic network connecting equilibria with two different orbit types.

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Section: Resultsmentioning

confidence: 76%

Bifurcation Diagrams and Heteroclinic Networks of Octagonal H-Planforms

Faye

Chossat

2012

J Nonlinear Sci

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“…The interaction of different modalities like emotion and cognition, which is important for the understanding of normal and pathological mental dynamics, can be described by the same type of equations [43,44]. It is important to emphasize that P i (r,t) may have a different sense relating to the performance of different cognitive, behavioural, tasks.…”

Section: (D) Basic Kinetic Modelmentioning

confidence: 99%

Hierarchical dynamics of informational patterns and decision-making

Varona

Rabinovich

2016

Proc. R. Soc. B.

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Traditional studies on the interaction of cognitive functions in healthy and disordered brains have used the analyses of the connectivity of several specialized brain networks-the functional connectome. However, emerging evidence suggests that both brain networks and functional spontaneous brain-wide network communication are intrinsically dynamic. In the light of studies investigating the cooperation between different cognitive functions, we consider here the dynamics of hierarchical networks in cognitive space. We show, using an example of behavioural decision-making based on sequential episodic memory, how the description of metastable pattern dynamics underlying basic cognitive processes helps to understand and predict complex processes like sequential episodic memory recall and competition among decision strategies. The mathematical images of the discussed phenomena in the phase space of the corresponding cognitive model are hierarchical heteroclinic networks. One of the most important features of such networks is the robustness of their dynamics. Different kinds of instabilities of these dynamics can be related to 'dynamical signatures' of creativity and different psychiatric disorders. The suggested approach can also be useful for the understanding of the dynamical processes that are the basis of consciousness.

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“…In ecological studies, the sequential unpredictable transitions of dominance between interacting species have been called a winnerless competition Rabinovich and Varona, 2011;Rabinovich et al, 2008Rabinovich et al, , 2010Rabinovich et al, , 2012. From the perspective of nonlinear dynamics, a mathematical image of these temporary 'victors' are saddle points, which attract the near trajectories along one direction and repel them along another direction in phase space (Hilborn et al, 1994).…”

Section: Modelmentioning

confidence: 99%