Autonomous learning by simple dynamical systems with delayed feedback

Kaluza, Pablo; Mikhailov, Alexander S.

doi:10.1103/physreve.90.030901

Cited by 10 publications

(14 citation statements)

References 25 publications

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“…The scheme facilitating this adaptive control in dynamical systems that exhibit chaos builds on the self-organized control of unstable periodic orbits through inclusion of a delayed intrinsic feedback [142]. Intriguingly, by application of this scheme to coupled Kuramoto oscillators, Kaluza & Mikhailov [143] were able to generate a system that robustly adapts desired synchronization levels through feedback control of coupling strengths. This corresponds to the adaptation of synaptic weights in a neural network (see §4d), highlighting that the combination of these rather general mechanisms can facilitate learning in addition to maintaining criticality.…”

Section: From Oscillations To Learningmentioning

confidence: 99%

Adaptive behaviour and learning in slime moulds: the role of oscillations

Boussard

Fessel

Oettmeier

et al. 2021

Phil. Trans. R. Soc. B

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The slime mould Physarum polycephalum , an aneural organism, uses information from previous experiences to adjust its behaviour, but the mechanisms by which this is accomplished remain unknown. This article examines the possible role of oscillations in learning and memory in slime moulds. Slime moulds share surprising similarities with the network of synaptic connections in animal brains. First, their topology derives from a network of interconnected, vein-like tubes in which signalling molecules are transported. Second, network motility, which generates slime mould behaviour, is driven by distinct oscillations that organize into spatio-temporal wave patterns. Likewise, neural activity in the brain is organized in a variety of oscillations characterized by different frequencies. Interestingly, the oscillating networks of slime moulds are not precursors of nervous systems but, rather, an alternative architecture. Here, we argue that comparable information-processing operations can be realized on different architectures sharing similar oscillatory properties. After describing learning abilities and oscillatory activities of P. polycephalum , we explore the relation between network oscillations and learning, and evaluate the organism's global architecture with respect to information-processing potential. We hypothesize that, as in the brain, modulation of spontaneous oscillations may sustain learning in slime mould. This article is part of the theme issue ‘Basal cognition: conceptual tools and the view from the single cell’.

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Section: From Oscillations To Learningmentioning

confidence: 99%

Adaptive behaviour and learning in slime moulds: the role of oscillations

Boussard

Fessel

Oettmeier

et al. 2021

Phil. Trans. R. Soc. B

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“…For example, one could think of minimizing the wiring length in the adaptive control of topology by complementing the method with optimal control theory [Lewis et al, 2012]. In [Kaluza and Mikhailov, 2014] an adaptive control scheme involving timedelayed feedback has been developed and applied to control zero-lag synchronization in oscillatory networks by changing the link strength. In principal, this method could also be applied in the control of cluster states and a comparison to the results obtained in Chapter 10 would be interesting.…”

Section: Discussionmentioning

confidence: 99%

Controlling Synchronization Patterns in Complex Networks

Lehnert¹

2016

Springer Theses

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In this thesis, I consider the control of synchronization in delay-coupled complex networks. As one main focus, several applications to neural networks will be discussed. In the first part, I focus on the stability of synchronization in complex networks meaning that the control is realized by considering the stability of synchrony in dependence on the parameters. In the second part, adaptive control of synchronization is studied. To this end, adaptive control algorithms are developed that tune the system parameters such that the desired control goal is reached.Besides zero-lag synchrony -a state where all nodes follow the same dynamics without a phase lag -groups and cluster states are considered, i.e., states where the network consists of several groups where the nodes within one group are in zero-lag synchrony and, in the case of cluster synchrony, with a constant phase lag between the clusters.The stability of synchronization can be accessed via the master stability function [Pecora and Carroll, 1998]. This convenient tool allows for treating the node dynamics and the network topology in two separate steps, and, thus, allows for a quite general treatment of different network topologies. In this thesis, I will discuss the generalization of the master stability function to group and cluster states and to non-smooth systems.The master stability function can be used to investigate synchrony in neural networks. Neurons are excitable systems where type-I and type-II excitability can be distinguished. Here, the stability of synchrony for both types in complex networks with excitatory and inhibitory links is investigated on two generic models, namely the normal form of the saddle-node infinite period bifurcation and the FitzHugh-Nagumo system. Furthermore, synchronization in systems with heterogeneous delays or node parameters is studied.In situations where parameters are unknown or drift, adaptive control methods are useful since they allow for an automatically realized adaption of the control parameters. A convenient adaptive method is the speed-gradient method that minimizes a predefined goal function [Fradkov, 1979[Fradkov, , 2007. I first apply this method in the control of an unstable focus and an unstable periodic orbit embedded in the Rössler attractor. Furthermore, I show that clusters states in networks of delayed coupled Stuart-Landau oscillators can be controlled by adaptively tuning the phase of the complex coupling strength or by adapting the topology. The first method is particularly simple because only one parameter has to be adapted, while the second method is more reliable in the sense that its success is widely independent of the choice of the control parameters and the initial conditions. ZUSAMMENFASSUNGIn dieser Arbeit wird die Kontrolle von Synchronisation in komplexen Netzwerken mit retardierten Kopplungen untersucht. Dabei werden verschiedene Anwendungen auf neuronale Netzwerke diskutiert. Der erste Teil der Arbeit beschäftigt sich mit der Stabilität von Synchronisation in komplexen Ne...

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“…The constant K τ determines the characteristic time for the evolution of the parameters and is equivalent to 1/τ . In this way, the new formulation replaces (3) with an iterative map as the new dynamics for w, and allows the system to evolve according to (1) during an interval of time T between successive iterations.…”

Section: A Discrete-time Formulationmentioning

confidence: 99%

“…The autonomous learning conjecture for the design of dynamical systems with predefined functionalities has been previously proposed by the authors [1]. It extends the dynamics of a given system to a new one where the parameters are transformed to dynamical variables.…”

Section: Introductionmentioning

confidence: 99%

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Autonomous learning by simple dynamical systems with a discrete-time formulation

Bilen¹,

Kaluza²

2017

Eur. Phys. J. B

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We present a discrete-time formulation for the autonomous learning conjecture.The main feature of this formulation is the possibility to apply the autonomous learning scheme to systems in which the errors with respect to target functions are not well-defined for all times. This restriction for the evaluation of functionality is a typical feature in systems that need a finite time interval to process a unit piece of information. We illustrate its application on an artificial neural network with feed-forward architecture for classification and a phase oscillator system with synchronization properties. The main characteristics of the discrete-time formulation are shown by constructing these systems with predefined functions.

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Autonomous learning by simple dynamical systems with delayed feedback

Cited by 10 publications

References 25 publications

Adaptive behaviour and learning in slime moulds: the role of oscillations

Adaptive behaviour and learning in slime moulds: the role of oscillations

Controlling Synchronization Patterns in Complex Networks

Autonomous learning by simple dynamical systems with a discrete-time formulation

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