Multistability in Spiking Neuron Models of Delayed Recurrent Inhibitory Loops

Ma, Jianfu; Wu, Jianhong

doi:10.1162/neco.2007.19.8.2124

Cited by 39 publications

(21 citation statements)

References 26 publications

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“…As with changes in synaptic strengths, the changes we observed in action potential propagation are also likely to influence computation, learning, and memory in neural systems. For example, changes in action potential delay alter the type and number of attractor states in recurrent delayed neural loops [48], [49] and neural networks [5]. Elucidating the cellular mechanisms of propagation plasticity is left to future work, but possibilities include non-uniform changes in ion channel properties [20], in the geometry of varicosities and branch points [36] or axonal arbors, in the proximity of glia [50], and in lipid membrane composition [51].…”

Section: Discussionmentioning

confidence: 99%

Long-Term Activity-Dependent Plasticity of Action Potential Propagation Delay and Amplitude in Cortical Networks

2008

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BackgroundThe precise temporal control of neuronal action potentials is essential for regulating many brain functions. From the viewpoint of a neuron, the specific timings of afferent input from the action potentials of its synaptic partners determines whether or not and when that neuron will fire its own action potential. Tuning such input would provide a powerful mechanism to adjust neuron function and in turn, that of the brain. However, axonal plasticity of action potential timing is counter to conventional notions of stable propagation and to the dominant theories of activity-dependent plasticity focusing on synaptic efficacies.Methodology/Principal FindingsHere we show the occurrence of activity-dependent plasticity of action potential propagation delays (up to 4 ms or 40% after minutes and 13 ms or 74% after hours) and amplitudes (up to 87%). We used a multi-electrode array to induce, detect, and track changes in propagation in multiple neurons while they adapted to different patterned stimuli in controlled neocortical networks in vitro. The changes did not occur when the same stimulation was repeated while blocking ionotropic gabaergic and glutamatergic receptors. Even though induction of changes in action potential timing and amplitude depended on synaptic transmission, the expression of these changes persisted in the presence of the synaptic receptor blockers.Conclusions/SignificanceWe conclude that, along with changes in synaptic efficacy, propagation plasticity provides a cellular mechanism to tune neuronal network function in vitro and potentially learning and memory in the brain.

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Section: Discussionmentioning

confidence: 99%

Long-Term Activity-Dependent Plasticity of Action Potential Propagation Delay and Amplitude in Cortical Networks

2008

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“…Although we approach the problem of an oscillator with pulsed feedback from a general perspective, not bound to a specific area of application, neurons with delayed feedback are a prototypical example for such systems. There exist some studies on this subject [41,[45][46][47]53], all of which have a common baseline: delay leads arXiv:1512.03567v1 [nlin.CD] 11 Dec 2015 to immense multistability. At first glance this result is not too surprising since multistability generically arises in delay differential equations due to a well-known mechanism called "periodic solution reappearance" [54].…”

Section: Introductionmentioning

confidence: 99%

Emergence and combinatorial accumulation of jittering regimes in spiking oscillators with delayed feedback

et al. 2015

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Interaction via pulses is common in many natural systems, especially neuronal. In this article we study one of the simplest possible systems with pulse interaction: a phase oscillator with delayed pulsatile feedback. When the oscillator reaches a specific state, it emits a pulse, which returns after propagating through a delay line. The impact of an incoming pulse is described by the oscillator's phase reset curve (PRC). In such a system we discover an unexpected phenomenon: for a sufficiently steep slope of the PRC, a periodic regular spiking solution bifurcates with several multipliers crossing the unit circle at the same parameter value. The number of such critical multipliers increases linearly with the delay and thus may be arbitrary large. This bifurcation is accompanied by the emergence of numerous "jittering" regimes with nonequal interspike intervals (ISIs). Each of these regimes corresponds to a periodic solution of the system with a period roughly proportional to the delay. The number of different "jittering" solutions emerging at the bifurcation point increases exponentially with the delay. We describe the combinatorial mechanism that underlies the emergence of such a variety of solutions. In particular, we show how a periodic solution exhibiting several distinct ISIs can imply the existence of multiple other solutions obtained by rearranging of these ISIs. We show that the theoretical results for phase oscillators accurately predict the behavior of an experimentally implemented electronic oscillator with pulsatile feedback.

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“…Equation (1.2) can describe the dynamics of a single neuron (or the mean field equation for a population of neurons in a network) with an excitatory and an inhibitory loop, having different delays. The pair of a positive and a negative delayed feedback occurs on the processing of sensory information and other processes in neuroscience (see [5,12,17,19] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Global dynamics of delay recruitment models with maximized lifespan

El-Morshedy

Röst

Ruiz-Herrera

2016

Z. Angew. Math. Phys.

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Abstract. We study the dynamics of the differential equationwith two delayed terms, representing a positive and a negative feedback. We prove delay-dependent and absolute global stability results for the trivial and for the positive equilibrium. Our theorems provide new mathematical results as well as novel insights for several biological systems, including three-stage populations, neural models with inhibitory and excitatory loops, and the blood platelet model of Bélair and Mackey. We show that, somewhat surprisingly, the introduction of a removal term with fixed delay in population models simplifies the dynamics of the equation.Mathematics Subject Classification. 39A30 · 39A33 · 37D45 · 92B20.

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Multistability in Spiking Neuron Models of Delayed Recurrent Inhibitory Loops

Cited by 39 publications

References 26 publications

Long-Term Activity-Dependent Plasticity of Action Potential Propagation Delay and Amplitude in Cortical Networks

Long-Term Activity-Dependent Plasticity of Action Potential Propagation Delay and Amplitude in Cortical Networks

Emergence and combinatorial accumulation of jittering regimes in spiking oscillators with delayed feedback

Global dynamics of delay recruitment models with maximized lifespan

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