Existence and stability of traveling pulses in a continuous neuronal network

SIAM Journal on Applied Dynamical Systems

Volumn 4, Issue 4, 2005, Pages 954-984

  Pintot, David J ^a   Jackson, Russell K ^b   Wayne, C Eugene ^b  

^a UNIVERSITY OF ROCHESTER   (United States)

^b USA   (United States)

Author keywords

Epileptic waves; Evans functions; Nonlocal equations

Indexed keywords

EPILEPTIC WAVES; EVANS FUNCTIONS; NONLOCAL EQUATIONS;

ELECTROMAGNETIC WAVE PROPAGATION; FUNCTIONS; INTEGRODIFFERENTIAL EQUATIONS; NEURAL NETWORKS; WAVE EFFECTS;

ELECTROMAGNETIC WAVES;

EID: 23944491928     PISSN: 15360040     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/040613020     Document Type: Article

References (16)

1. P. C. BRESSLOFF AND S. E. FOLIAS, Front bifurcations in an excitatory neural network, SIAM J. Appl. Math., 65 (2004), pp. 131-151.
2. S. COOMBES, G. S. LORD, AND M. R. OWEN, Waves and bumps in neuronal networks with axo-dendritic synaptic interactions, Phys. D, 178 (2003), pp. 219-241.
3. S. COOMBES, Dynamics of synapticalty coupled integrate-and-fire-or-burst neurons, Phys. Rev. E (3), 67 (2003), 041910.
4. S. COOMBES AND M. R. OWEN, Evans functions for integral neural field equations with Heaviside firing rate function, SIAM J. Appl. Dyn. Syst., 3 (2004), pp. 574-600.
5. B. ERMENTROUT AND J. MCLEOD, Existence and uniqueness of traveling waves for a neural network, Proc. Roy. Soc. Edinburgh Sect. A, 123 (1993), pp. 461-478.
6. D. GOLOMB AND Y. AMITAI, Propagating neuronal discharges in neocortical slices: Computational and experimental study, J. Neurophysiol., 78 (1997), pp. 1199-1211.
7. D. GOLOMB, Models of neuronal transient synchrony during propagation of activity through neocortical circuitry, J. Neurophysiol., 79 (1998), pp. 1-12.
8. J. JALICS, Slow waves in mutually inhibitory neuronal networks, Phys. D, 192 (2004), pp. 95-122.
9. T. KAPITULA, N. KUTZ, AND B. SANDSTEDE, The Evans function for nonlocal equations, Indiana Univ. Math. J., 53 (2004), pp. 1095-1126.
10. C. R. LAING AND W. C. TROY, PDE methods for nonlocal models, SIAM J. Appl. Dyn. Syst., 2 (2003), pp. 487-516.
11. D. J. PINTO AND G. B. ERMENTROUT, Spatially structured activity in synapticdlly coupled neuronal networks, I. Traveling fronts and pulses, II. Lateral inhibition and standing pulses, SIAM J. Appl. Math., 62 (2001), pp. 206-243.
12. D. J. PINTO, S. A. PATRICK, H. W. HUANG, AND B. W. CONNORS, Initiation, propagation, and termination of epileptiform activity in rodent neocortex in vitro involve distinct mechanisms, J. Neurosci., 25 (2005), pp. 8131-8140.
13. J. RINZEL AND D. TERMAN, Propagation phenomena in a bistable reaction-diffusion system, SIAM J. Appl. Math., 42 (1982), pp. 1111-1137.
14. J. RUBIN, A nonlocal eigenvalue problem for the stability of a traveling wave in a neuronal medium, Discrete Contin. Dyn. Syst., 10 (2004), pp. 925-940.
15. J. Y. WU, L. GUAN, AND Y. TSAU, Propagating activation during oscillations and evoked responses in neocortical slices, J. Neurosci., 19 (1999), pp. 5005-5015.
16. L. ZHANG, On stability of traveling wave solutions in synaptically coupled neuronal networks, Differential Integral Equations, 16 (2003), pp. 513-536.