Computation by Switching in Complex Networks of States

Neves, Fábio Schittler; Timme, Marc

doi:10.1103/physrevlett.109.018701

Cited by 56 publications

(39 citation statements)

References 32 publications

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“…Dynamics involving switching transitions between transiently stable states has been addressed in the contexts of semantic learning in autonomously active networks [13,14], within reservoir computing [15] and in networks dominated by heteroclinic orbits [16]. In case of the latter, periodic orbits are formed when the dynamics follows heteroclinic connections between saddle points encoding information in the different states, which however exist only for symmetry-invariant networks.…”

Section: Introductionmentioning

confidence: 99%

Attractor metadynamics in terms of target points in slow-fast systems: adiabatic versus symmetry protected flow in a recurrent neural network

2018

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In dynamical systems with distinct time scales the time evolution in phase space may be influenced strongly by the fixed points of the fast subsystem. Orbits then typically follow these points, performing in addition rapid transitions between distinct branches on the time scale of the fast variables. As the branches guide the dynamics of a system along the manifold of former fixed points, they are considered transiently attracting states and the intermittent transitions between branches correspond to state switching within transient-state dynamics. A full characterization of the set of former fixed points, the critical manifold, tends to be difficult in high-dimensional dynamical systems such as large neural networks. Here we point out that an easily computable subset of the critical manifold, the set of target points, can be used as a reference for the investigation of high-dimensional slow-fast systems. The set of target points corresponds in this context to the adiabatic projection of a given orbit to the critical manifold. Applying our framework to a simple recurrent neural network, we find that the scaling relation of the Euclidean distance between the trajectory and its target points with the control parameter of the slow time scale allows to distinguish an adiabatic regime from a state that is effectively independent from target points.

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Section: Introductionmentioning

confidence: 99%

Attractor metadynamics in terms of target points in slow-fast systems: adiabatic versus symmetry protected flow in a recurrent neural network

2018

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“…Mathematical analysis of interaction networks are valuable in understanding the dynamics of complex systems [1][2][3][4][5]. Concurrent antagonism, where every component of the system simultaneously represses each other, is one of the interaction systems that approximate many natural phenomena.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium switching and mathematical properties of nonlinear interaction networks with concurrent antagonism and self-stimulation

Rabajante

Talaue

2015

Chaos, Solitons & Fractals

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“…In particular, points arbitrarily close to an unstable attractor can approach another unstable attractor, forming heteroclinic connections [46,47,48]. As a result, switching among the attractors can occur following the natural dynamical evolution, into which information reflecting the input signal can be encoded [49]. If the system possesses a large number of unstable attractors, they can form a complex network through heteroclinic connections in the phase space, which can be exploited for complex logical computation [50,49].…”

Section: Introductionmentioning

confidence: 99%

Partially unstable attractors in networks of forced integrate-and-fire oscillators

Zou

Deng

et al. 2017

Nonlinear Dyn

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The asymptotic attractors of a nonlinear dynamical system play a key role in the long-term physically observable behaviors of the system. The study of attractors and the search for distinct types of attractor have been a central task in nonlinear dynamics. In smooth dynamical systems, an attractor is often enclosed completely in its basin of attraction with a finite distance from the basin boundary. Recent works have uncovered that, in neuronal networks, unstable attractors with a remote basin can arise, where almost every point on the attractor is locally transversely repelling. Herewith we report our discovery of a class of attractors: partially unstable attractors, in pulsecoupled integrate-and-fire networks subject to a periodic forcing. The defining feature of such an attractor is that it can simultaneously possess locally stable and unstable sets, both of positive measure. Exploiting the structure of the key dynamical events in the network, we develop a symbolic analysis that can fully explain the emergence of the partially unstable attractors. To

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Computation by Switching in Complex Networks of States

Cited by 56 publications

References 32 publications

Attractor metadynamics in terms of target points in slow-fast systems: adiabatic versus symmetry protected flow in a recurrent neural network

Attractor metadynamics in terms of target points in slow-fast systems: adiabatic versus symmetry protected flow in a recurrent neural network

Equilibrium switching and mathematical properties of nonlinear interaction networks with concurrent antagonism and self-stimulation

Partially unstable attractors in networks of forced integrate-and-fire oscillators

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