Stable Irregular Dynamics in Complex Neural Networks
Abstract
Irregular dynamics in multidimensional systems is commonly associated with chaos. For infinitely large sparse networks of spiking neurons, mean field theory shows that a balanced state of highly irregular activity arises under various conditions. Here we analytically investigate the microscopic irregular dynamics in finite networks of arbitrary connectivity, keeping track of all individual spike times. For delayed, purely inhibitory interactions we demonstrate that any irregular dynamics that characterizes the balanced state is not chaotic but rather stable and convergent towards periodic orbits. These results highlight that chaotic and stable dynamics may be equally irregular.
- Publication:
-
Physical Review Letters
- Pub Date:
- February 2008
- DOI:
- 10.1103/PhysRevLett.100.048102
- arXiv:
- arXiv:0705.3214
- Bibcode:
- 2008PhRvL.100d8102J
- Keywords:
-
- 87.18.Sn;
- 05.45.-a;
- 87.10.-e;
- Neural networks;
- Nonlinear dynamics and chaos;
- General theory and mathematical aspects;
- Condensed Matter - Disordered Systems and Neural Networks
- E-Print:
- 10 pages, 2 figures