### Abstract

In this paper, we discuss how an analog signal can be encoded using biophysically realistic neural networks. Using the activity curve of a single neuron, we argue that the activities can be pooled over a population so that the weighted sum of the activities approximate a given function. Since the activities of neurons are not available as a variable, we propose to generate them in real time by a suitable low-pass filter. Using the proposed scheme, we demonstrate how simple ordinary differential equations can be solved. In effect, the ordinary differential equations are solved by dynamically updating the activities of the neurons. In an actual biological neural network, the activities of the cells are not obtained by a low-pass filter. They are integrated in the network by a suitable synaptic input. A new optimization algorithm for finding a set of optimal synaptic weights has been proposed and successfully implemented using a software package GENESIS. The difference between biological neural networks and artificial neural networks is discussed in somewhat greater details. The important concepts are illustrated by implementing a memory and by solving a periodic ordinary differential equation, the Van der Pol oscillator.

Original language | English |
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Pages (from-to) | 181-196 |

Number of pages | 16 |

Journal | Mathematical and Computer Modelling |

Volume | 39 |

Issue number | 2-3 |

DOIs | |

State | Published - Jan 2004 |

### Keywords

- Limit cycles
- Neural networks
- Neuroscience
- Oscillations
- Rate coding

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## Cite this

*Mathematical and Computer Modelling*,

*39*(2-3), 181-196. https://doi.org/10.1016/S0895-7177(04)90006-4