Sensitive Signal Detection Using a Feed-Forward Oscillator Network

McCullen, Nick; Mullin, T.; Golubitsky, Martin

doi:10.1103/physrevlett.98.254101

Cited by 26 publications

(20 citation statements)

References 25 publications

(22 reference statements)

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“…Chinese Sci Bull, 2011Bull, , 56: 3623-3629, doi: 10.1007 Systems that can detect and amplify signals at specific frequencies are commonplace in the natural world and most notably in the visual and auditory systems of animals [1]. Signal detection in animals is through light-and auralsensitive organs, constituted by a large number of networked units.…”

Section: Citationmentioning

confidence: 99%

“…Stoop et al suggested a van-der-Pol oscillator model to explain the active signal amplification in the Drosophila hearing system [4]. McCullen et al claimed that the generalized van-der-Pol oscillator with a 3-cell feed-forward network can explain the signal amplification well [1]. In detail, a double-well potential may be used to show how self-tuning works [10].…”

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Signal response amplification of scale-free networks

Liu

2011

Chin. Sci. Bull.

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In many animals and insects, hearing is very acute to the faintest of sounds; the underlying mechanism can be explained by self-tuning. Recently, signal response amplification has been shown to be implemented through networks exhibiting scale-free topology, which has potential applications in artificial information processing systems and devices. We review in this paper the main results obtained in networked double-well oscillators and briefly discuss future research directions.signal response, scale-free network, self-tuning, double-well oscillator Citation:Liu Z H. Signal response amplification of scale-free networks. Chinese Sci Bull, 2011Bull, , 56: 3623-3629, doi: 10.1007 Systems that can detect and amplify signals at specific frequencies are commonplace in the natural world and most notably in the visual and auditory systems of animals [1]. Signal detection in animals is through light-and auralsensitive organs, constituted by a large number of networked units. For example, cells in living organisms respond to their environment by an interconnected network of receptors, messengers, protein kinases and other signaling molecules [2][3][4]. One of the more prominent features of our hearing system is the ability to perceive sound stimuli that range over six orders of magnitude in sound pressure [5]. Hair cells within the cochlear are stimulated by sound waves, the induced motion being amplified at characteristic locations that depends on the frequencies of sound. These cells transmit signals to the auditory nerve [6]. It is well known that many animals and insects have the ability to detect faint sounds from their environment. Physiological evidence exists for a range of animals and insect auditory systems that this active audition is due to Hopf bifurcations [7][8][9]. Models have also been proposed to develop the underlying mechanism behind enhanced amplification in hearing systems, i.e. self-tuned critical oscillations of hair cells nearby the Hopf bifurcation. 2 , where a controls the barrier height of the potential; x=±1 are the locations of the two minima. Suppose an oscillator has probability w + (w  ) of jumping from the right (left) well to the left (right) well; then self-tuning means that the parameter a can be self-adjusted by the following equation: a t a t w t p t w t p t twhere p + (p  ) denotes the probability that the oscillator stays at x=±1. If w + and w  are small, the first term in eq.(1) will be larger than the second term and thus result in a decrease in a. For larger w + and w  , the first term in eq.(1) will be smaller than the second term and thus result in an increase in a. Therefore, the parameter a is self-tuned to an optimal value by switching probabilities w + and w  . Scientists and engineers frequently take inspiration from

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Section: Citationmentioning

confidence: 99%

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confidence: 99%

Signal response amplification of scale-free networks

Liu

2011

Chin. Sci. Bull.

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“…The amplification and tuning properties of the human hair cells have been modelled by systems near a Hopf bifurcation . A Hopf bifurcation generates a small amplitude oscillation, in a nonlinear system, as a parameter is varied.…”

Section: Introductionmentioning

confidence: 99%

“…Cells behaving qualitatively similarly to the van der Pol oscillator have been used to obtain the amplification of the signal in some of these models . Stoop et al use a generalization of the van der Pol oscillator to model the antennal hearing organs of the fruit fly Drosophila melanogaster .…”

Section: Introductionmentioning

confidence: 99%

A note on fractional feed‐forward networks

Pinto

2016

Math Methods in App Sciences

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We simulate a fractional feed-forward network. This network consists of three coupled identical 'cells' (aka, oscillators). We study the behaviour of the associated coupled cell system for variation of the order of the fractional derivative, 0 < < 1. We consider the Caputo derivative, approximated by the Grünwald-Letnikov approach, using finite differences of fractional order. There is observed amplification of the small signals by exploiting the nonlinear response of each oscillator near its intrinsic Hopf bifurcation point for each value of˛. The value of the Hopf bifurcation point varies with the order of the fractional derivative˛.

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“…102 A potential application of this behavior is to the design of a nonlinear filter which selects oscillations close to a specific frequency and amplifies them. 58 Experimental proof-ofconcept can be found in McCullen et al 90 …”

Section: Anomalous Growth In Network Hopf Bifurcationmentioning

confidence: 99%

Recent advances in symmetric and network dynamics

Golubitsky

Stewart

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We summarize some of the main results discovered over the past three decades concerning symmetric dynamical systems and networks of dynamical systems, with a focus on pattern formation. In both of these contexts, extra constraints on the dynamical system are imposed, and the generic phenomena can change. The main areas discussed are time-periodic states, mode interactions, and non-compact symmetry groups such as the Euclidean group. We consider both dynamics and bifurcations. We summarize applications of these ideas to pattern formation in a variety of physical and biological systems, and explain how the methods were motivated by transferring to new contexts Rene Thom's general viewpoint, one version of which became known as "catastrophe theory." We emphasize the role of symmetry-breaking in the creation of patterns. Topics include equivariant Hopf bifurcation, which gives conditions for a periodic state to bifurcate from an equilibrium, and the H/K theorem, which classifies the pairs of setwise and pointwise symmetries of periodic states in equivariant dynamics. We discuss mode interactions, which organize multiple bifurcations into a single degenerate bifurcation, and systems with non-compact symmetry groups, where new technical issues arise. We transfer many of the ideas to the context of networks of coupled dynamical systems, and interpret synchrony and phase relations in network dynamics as a type of pattern, in which space is discretized into finitely many nodes, while time remains continuous. We also describe a variety of applications including animal locomotion, Couette-Taylor flow, flames, the Belousov-Zhabotinskii reaction, binocular rivalry, and a nonlinear filter based on anomalous growth rates for the amplitude of periodic oscillations in a feed-forward network. Symmetry is a feature of many systems of interest in applied science. Mathematically, a symmetry is a transformation that preserves structure; for example, a square looks unchanged if it is rotated through any multiple of a right angle, or reflected in a diagonal or a line joining the midpoints of oppose edges. These symmetries also appear in mathematical models of real-world systems, and their effect is often extensive. The last thirty to forty years has seen considerable advances in the mathematical understanding of the effects of symmetry on dynamical systems-systems of ordinary differential equations. In general, symmetry leads to pattern formation, via a mechanism called symmetry-breaking. For example, if a system with circular symmetry has a time-periodic state, repeating the same behavior indefinitely, then typically this state is either a standing wave or a rotating wave. This observation applies to the movement of a flexible hosepipe as water passes through it: in the standing wave, the hosepipe moves to and fro like a pendulum; in the rotating wave, it goes round and round with its end describing a circle. This observation also applies to how flame fronts move on a circular burner. We survey some basic mathematical ideas that have ...

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Sensitive Signal Detection Using a Feed-Forward Oscillator Network

Cited by 26 publications

References 25 publications

Signal response amplification of scale-free networks

Signal response amplification of scale-free networks

A note on fractional feed‐forward networks

Recent advances in symmetric and network dynamics

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