Chaotic itinerancy

Kaneko, Kunihiko; Tsuda, Ichiro

doi:10.1063/1.1607783

Cited by 210 publications

(145 citation statements)

References 49 publications

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“…Much of this work rests on uniform coupling, which induces a synchronisation manifold, around which the dynamics play. The ensuing chaotic itinerancy has many intriguing aspects that can be related to neuronal systems (Breakspear et al, 2003;Kaneko and Tsuda, 2003). However, the focus of this work is not chaotic itinerancy but chaotic transience (the transient dynamics evoked by perturbations to the systems state) in systems with asymmetric coupling.…”

Section: Hierarchical Modelsmentioning

confidence: 99%

Modelling event-related responses in the brain

2005

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The aim of this work was to investigate the mechanisms that shape evoked electroencephalographic (EEG) and magneto-encephalographic (MEG) responses. We used a neuronally plausible model to characterise the dependency of response components on the models parameters. This generative model was a neural mass model of hierarchically arranged areas using three kinds of inter-area connections (forward, backward and lateral). We investigated how responses, at each level of a cortical hierarchy, depended on the strength of connections or coupling. Our strategy was to systematically add connections and examine the responses of each successive architecture. We did this in the context of deterministic responses and then with stochastic spontaneous activity. Our aim was to show, in a simple way, how event-related dynamics depend on extrinsic connectivity. To emphasise the importance of nonlinear interactions, we tried to disambiguate the components of event-related potentials (ERPs) or event-related fields (ERFs) that can be explained by a linear superposition of trial-specific responses and those engendered nonlinearly (e.g., by phase-resetting). Our key conclusions were; (i) when forward connections, mediating bottom-up or extrinsic inputs, are sufficiently strong, nonlinear mechanisms cause a saturation of excitatory interneuron responses. This endows the system with an inherent stability that precludes nondissipative population dynamics. (ii) The duration of evoked transients increases with the hierarchical depth or level of processing. (iii) When backward connections are added, evoked transients become more protracted, exhibiting damped oscillations. These are formally identical to late or endogenous components seen empirically. This suggests that late components are mediated by reentrant dynamics within cortical hierarchies. (iv) Bilateral connections produce similar effects to backward connections but can also mediate zero-lag phase-locking among areas. (v) Finally, with spontaneous activity, ERPs/ERFs can arise from two distinct mechanisms: For low levels of (stimulus related and ongoing) activity, the systems response conforms to a quasi-linear superposition of separable responses to the fixed and stochastic inputs. This is consistent with classical assumptions that motivate trial averaging to suppress spontaneous activity and disclose the ERP/ ERF. However, when activity is sufficiently high, there are nonlinear interactions between the fixed and stochastic inputs. This interaction is expressed as a phase-resetting and represents a qualitatively different explanation for the ERP/ERF. D 2004 Elsevier Inc. All rights reserved.Keywords: Electroencephalography; Magnetoencephalography; Neural networks; Nonlinear dynamics; Causal modelling IntroductionClassical event-related potentials (ERPs) and event-related fields (ERFs) have been used for decades as putative electrophysiological correlates of perceptual and cognitive operations. However, the exact neurobiological mechanisms underlying their generation are largely unk...

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Section: Hierarchical Modelsmentioning

confidence: 99%

Modelling event-related responses in the brain

2005

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“…In the parameter space between the coherence regions the network dynamics remain coherent but not periodic anymore. The states alternate chaotically between the adjacent k-states and thus exhibit chaotic itineracy [6,22]. The combination of period-adding in space and period-doubling in time represents a remarkable feature of networks of coupled chaotic oscillators with nonlocal coupling.…”

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confidence: 99%

Loss of Coherence in Dynamical Networks: Spatial Chaos and Chimera States

et al. 2011

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We discuss the breakdown of spatial coherence in networks of coupled oscillators with nonlocal interaction. By systematically analyzing the dependence of the spatio-temporal dynamics on the range and strength of coupling, we uncover a dynamical bifurcation scenario for the coherence-incoherence transition which starts with the appearance of narrow layers of incoherence occupying eventually the whole space. Our findings for coupled chaotic and periodic maps as well as for time-continuous Rössler systems reveal that intermediate, partially coherent states represent characteristic spatiotemporal patterns at the transition from coherence to incoherence. Understanding the dynamics on networks is at the heart of modern nonlinear science and has a wide applicability to various fields [1,2]. Thus, network science is a vibrant, interdisciplinary research area with strong connections to physics. For example, concepts of theoretical physics like the Turing instability, which is a known paradigm of non-equilibrium self-organization in spacecontinuous systems, have recently been transferred to complex networks [3]. While spatially extended systems show pattern formation mediated by diffusion, i.e., local interactions, a network takes also into account long-range and global interactions yielding more realistic spatial geometries.Network topologies like all-to-all coupling of, for instance, phase oscillators (Kuramoto model) or chaotic maps (Kaneko model) were intensively studied , and numerous characteristic regimes were found [4][5][6]. In particular, for globally coupled chaotic maps they rangefor decreasing coupling strength -from complete chaotic synchronization via clustering and chaotic itineracy to complete desynchronization. The opposite case, i.e., nearest-neighbor coupling, is known as lattice dynamical systems of time-continuous oscillators, or coupled map lattices if the oscillator dynamics is discrete in time. These kinds of networks arise naturally as discrete approximation of systems with diffusion and have also been thoroughly studied. They can demonstrate rich dynamics such as solitons, kinks, etc. up to fully developed spatiotemporal chaos [6][7][8][9][10].The case of networks with nonlocal coupling, however, has been much less studied in spite of numerous applications in different fields. Characteristic examples pertain to neuroscience [11,12], chemical oscillators [13,14], electrochemical systems [15], and Josephson junctions [16]. A new impulse to study such networks was given, in particular, by the discovery of so-called chimera states [17,18]. The main peculiarity of these spatio-temporal patterns is that they have a hybrid spatial structure, partially coherent and partially incoherent, which can develop in networks of identical oscillators without any sign of inhomogeneity.In this Letter we discuss the transition between coherent and incoherent dynamics in networks of nonlocally coupled oscillators. We start with coupled chaotic mapswhere z i are real dynamic variables (i = 1, ..., N , N 1 and the inde...

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“…Artificial neural networks for chaotic itinerancy were studied with great interests (Aihara et al 1990;Tsuda 1991Tsuda , 2001Kaneko and Tsuda 2003;Fuji et al 1996). As one of those works, by Nara and Davis, chaotic dynamics was introduced in a recurrent neural network model (RNNM) consisting of binary neurons, and for investigating the functional aspects of chaos, they have applied chaotic dynamics by means of numerical methods to solving, for instance, a memory search task which is set in an ill-posed context (Nara andDavis 1992, 1997;Nara et al 1993Nara et al , 1995Kuroiwa et al 1999;Suemitsu and Nara 2003).…”

Section: Introductionmentioning

confidence: 99%

Novel tracking function of moving target using chaotic dynamics in a recurrent neural network model

Nara

2007

Cogn Neurodyn

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Chaotic dynamics introduced in a recurrent neural network model is applied to controlling an object to track a moving target in two-dimensional space, which is set as an ill-posed problem. The motion increments of the object are determined by a group of motion functions calculated in real time with firing states of the neurons in the network. Several cyclic memory attractors that correspond to several simple motions of the object in twodimensional space are embedded. Chaotic dynamics introduced in the network causes corresponding complex motions of the object in two-dimensional space. Adaptively real-time switching of control parameter results in constrained chaos (chaotic itinerancy) in the state space of the network and enables the object to track a moving target along a certain trajectory successfully. The performance of tracking is evaluated by calculating the success rate over 100 trials with respect to nine kinds of trajectories along which the target moves respectively. Computer experiments show that chaotic dynamics is useful to track a moving target. To understand the relations between these cases and chaotic dynamics, dynamical structure of chaotic dynamics is investigated from dynamical viewpoint.

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Chaotic itinerancy

Cited by 210 publications

References 49 publications

Modelling event-related responses in the brain

Modelling event-related responses in the brain

Loss of Coherence in Dynamical Networks: Spatial Chaos and Chimera States

Novel tracking function of moving target using chaotic dynamics in a recurrent neural network model

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