Transient regime duration in continuous-time neural networks with delay

Pakdaman, Khashayar; Ragazzo, Clodoaldo Grotta; Malta, C. P.

doi:10.1103/physreve.58.3623

Cited by 57 publications

(43 citation statements)

References 39 publications

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“…This bimodal nature of the distribution in L is related to the number of delayed zero crossings, since if x (t) and x (tKt) have different signs, then there is an increased probability that the evolution of (4.1) will change direction, thus further increasing the time until threshold crossing (Milton et al 2008). In other words, the slower paths arise because the solution is temporarily confined near the origin as reported previously in delay differential equations in the setting of a saddle point (Pakdaman et al 1998;Grotta-Ragazzo et al 1999).…”

Section: First-passage Timesmentioning

confidence: 74%

Balancing with positive feedback: the case for discontinuous control

Milton

Townsend

King

et al. 2009

Phil. Trans. R. Soc. A.

103

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Experimental observations indicate that positive feedback plays an important role for maintaining human balance in the upright position. This observation is used to motivate an investigation of a simple switch-like controller for postural sway in which corrective movements are made only when the vertical displacement angle exceeds a certain threshold. This mechanism is shown to be consistent with the experimentally observed variations in the two-point correlation for human postural sway. Analysis of first-passage times for this model suggests that this control strategy may slow escape by taking advantage of two intrinsic properties of a stochastic unstable first-order delay differential equation: (i) time delay and (ii) the possibility that the dynamics can be 'temporarily confined' near the origin.

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Section: First-passage Timesmentioning

confidence: 74%

Balancing with positive feedback: the case for discontinuous control

Milton

Townsend

King

et al. 2009

Phil. Trans. R. Soc. A.

103

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“…Analogous situations in which eigenvalues with both negative and positive real parts co-exist arise when τ = 0 in the setting of a saddle point [12,13,16,21] or Hopf bifurcation [46] and may, in part, explain the stabilizing effects of noise in these situations. Numerical simulations suggest that similar phenomena occur for τ = 0 and account for the postponement of Hopf bifurcations [18] and delay-induced transient oscillations [47,48]. The nervous system must necessarily contend with the effects of time delays and noise.…”

Section: -P4mentioning

confidence: 79%

Unstable dynamical systems: Delays, noise and control

Milton¹,

Cabrera²,

Ohira³

2008

Europhys. Lett.

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Escape from an unstable fixed point in a time-delayed dynamical system in the presence of additive white noise depends on both the magnitude of the time delay, τ , and the initial function. In particular, the longer the delay the smaller the variance and hence the slower the rate of escape. Numerical simulations demonstrate that the distribution of first passage times is bimodal, the longest first passage times are associated with those initial functions that cause the greatest number of delayed zero crossings, i.e. instances where the deviations of the controlled variable from the fixed point at times t and t − τ have opposite signs. These observations support the utility of control strategies using pulsatile stimuli triggered only when variables exceed certain thresholds.

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“…The aspect of dynamical stability in the presence of noise has been a central question, and this two-neuron model system has been used to approach it in a simple and analytically accessible way (25) (for a list of references on the stability of two-neuron systems, see reference 2 in ref. 26). With delay as a potential source of oscillations, a well studied stability criterion has been the case of absence of oscillations (25), similar to stable fixed points in artificial neural networks with symmetric weights.…”

Section: Feedback Loops Of Two Nodesmentioning

confidence: 99%

“…With delay as a potential source of oscillations, a well studied stability criterion has been the case of absence of oscillations (25), similar to stable fixed points in artificial neural networks with symmetric weights. In networks with asymmetric weights, long transients occur easily (26).…”

Section: Feedback Loops Of Two Nodesmentioning

confidence: 99%

Topology of biological networks and reliability of information processing

Klemm

Bornholdt

2005

Proc. Natl. Acad. Sci. U.S.A.

170

124

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Survival of living cells and organisms is largely based on highly reliable function of their regulatory networks. However, the elements of biological networks, e.g., regulatory genes in genetic networks or neurons in the nervous system, are far from being reliable dynamical elements. How can networks of unreliable elements perform reliably? We here address this question in networks of autonomous noisy elements with fluctuating timing and study the conditions for an overall system behavior being reproducible in the presence of such noise. We find a clear distinction between reliable and unreliable dynamical attractors. In the reliable case, synchrony is sustained in the network, whereas in the unreliable scenario, fluctuating timing of single elements can gradually desynchronize the system, leading to nonreproducible behavior. The likelihood of reliable dynamical attractors strongly depends on the underlying topology of a network. Comparing with the observed architectures of gene regulation networks, we find that those 3-node subgraphs that allow for reliable dynamics are also those that are more abundant in nature, suggesting that specific topologies of regulatory networks may provide a selective advantage in evolution through their resistance against noise.genetic networks ͉ biological computation ͉ robustness ͉ stability ͉ computer model

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Transient regime duration in continuous-time neural networks with delay

Cited by 57 publications

References 39 publications

Balancing with positive feedback: the case for discontinuous control

Balancing with positive feedback: the case for discontinuous control

Unstable dynamical systems: Delays, noise and control

Topology of biological networks and reliability of information processing

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