Distributed Nonlocal Feedback Delays May Destabilize Fronts in Neural Fields, Distributed Transmission Delays Do Not

Hutt, Axel; Zhang, Linghai

doi:10.1186/2190-8567-3-9

Cited by 8 publications

(1 citation statement)

References 47 publications

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“…However, in many real situations the time delays are not constant; they may change over time and/or depend on system parameters [23,24]. In the context of neural networks, the presence of many parallel pathways with different axon sizes and lengths results in different distributions of transmission velocities, which can be studied using models with distributed time delays [25,26,27].…”

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confidence: 99%

Dynamics of Neural Systems with Discrete and Distributed Time Delays

Rahman¹,

Blyuss²,

Kyrychko³

2015

SIAM J. Appl. Dyn. Syst.

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Abstract. In real-world systems, interactions between elements do not happen instantaneously, due to the time required for a signal to propagate, reaction times of individual elements, and so forth. Moreover, time delays are normally nonconstant and may vary with time. This means that it is vital to introduce time delays in any realistic model of neural networks. In order to analyze the fundamental properties of neural networks with time-delayed connections, we consider a system of two coupled two-dimensional nonlinear delay differential equations. This model represents a neural network, where one subsystem receives a delayed input from another subsystem. An exciting feature of the model under consideration is the combination of both discrete and distributed delays, where distributed time delays represent the neural feedback between the two subsystems, and the discrete delays describe the neural interaction within each of the two subsystems. Stability properties are investigated for different commonly used distribution kernels, and the results are compared to the corresponding results on stability for networks with no distributed delays. It is shown how approximations of the boundary of the stability region of a trivial equilibrium can be obtained analytically for the cases of delta, uniform, and weak gamma delay distributions. Numerical techniques are used to investigate stability properties of the fully nonlinear system, and they fully confirm all analytical findings.

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confidence: 99%