Oscillation death in a two-neuron network with delay in a self-connection

Journal of Biological Systems

Volumn 15, Issue 1, 2007, Pages 49-61

  Monteiro, L H A ^a,b   Pellizari Filho, A ^a   Chaui Berlinck, J G ^b   Piqueira, J R C ^b  

^a MACKENZIE PRESBYTERIAN UNIVERSITY   (Brazil)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Hopfield Model; Olfactory Bulb; Self Sustained Oscillation; Two Neuron Network

Indexed keywords

EID: 33847353397     PISSN: 02183390     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218339007002052     Document Type: Article

References (38)

1. Arbib MA (ed.), The Handbook of Brain Theory and Neural Networks, The MIT Press, Cambridge, MA, 1998.
2. Monteiro LHA, Bussab MA, Chaui-Berlinck JG, Analytical results on a Wilson-Cowan neuronal network modified model, J Theor Biol 219:83-91, 2002.
3. Monteiro LHA, Canto NCF, Chaui-Berlinck JG, Orsatti FM, Piqueira JRC, Global and partial synchronism in phase-locked loop networks, IEEE Trans Neural Netw. 14:1572-1575, 2003.
4. Das P, Mukherjee D, Hopf bifurcation and permanence analysis of an S-I epidemic model with delay, J Biol Syst 12:169-177, 2004.
5. Wu FX, Zhang WJ, Kusalik AJ, State-space model with time delays for gene regulatory networks, J Biol Syst 12:483-500, 2004.
6. Bennett DL, Gourley SA, Asymptotic properties of a delay differential equation model for the interaction of glucose with plasma and interstitial insulin, Appl Math Comput 151:189-207, 2004.
7. Guckenheimer J, Holmes P, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer, New York, 1983.
8. Hopfield JJ, Tank DW, Computing with neural circuits: a model, Science 233:625-633, 1986.
9. Babcock KL, Westervelt RM, Dynamics of simple electronic neural networks, Physica D 28:305-316, 1987.
10. Gopalsamy K, Leung I, Delay induced periodicity in a neural netlet of excitation and inhibition, Physica D 89:395-426, 1996.
11. Olien L, Bélair J, Bifurcations, stability, and monotonicity properties of a delayed neural network model, Physica D 102:349-363, 1997.
12. Wei J, Ruan S, Stability and bifurcation in a neural network model with two delays, Physica D 130:255-272, 1999.
13. Pakdaman K, Grotta-Ragazzo C, Malta CP, Arino O, Vibert JF, Effect of delay on the boundary of the basin of attraction in a system of two neurons, Neural Netw 11:509-519, 1998.
14. Chen Y, Wu J, Slowly oscillating periodic solutions for a delayed frustrated network of two neurons, J Math Anal Appl 259:188-208, 2001.
15. Liang XB, Equivalence between local exponential stability of the unique equilibrium point and global stability for Hopfield-type neural networks with two neurons, IEEE Trans Neural Netw 11:1194-1196, 2000.
16. Guo S, Huang L, Periodic solutions in an inhibitory two-neuron network, J Comp Appl Math 161:217-229, 2003.
17. Wilson HR, Cowan JD, Excitatory and inhibitory interactions in localized populations of model neurons, Biophys J 12:1-24, 1972.
18. Ramana Reddy DV, Sen A, Johnson GL, Time delay induced death in coupled limit cycle oscillations, Phys Rev Lett 80:5109-5122, 1998.
19. Engel AK, König P, Kreiter AK, Schillen TB, Singer W, Temporal coding in the visual cortex: new vistas on integration in the nervous system, Trends Neurosci 15:218-226, 1992.
20. Selverston AI, Moulins M, Oscillatory neural networks, Ann Rev Physiol 47:29-48, 1985.
21. Baird B, Nonlinear dynamics of pattern formation and pattern recognition in the rabbit olfactory bulb, Physica D 22:150-175, 1986.
22. Dowling JE, Retinal processing of vision, in Greger R, Windhorst U (eds.), Comprehensive Human Physiology: From Cellular Mechanisms to Integration, Springer, Berlin, Vol. 1, Ch. 38, 1996.
23. Windhorst U, Spinal cord and brainstem: motor output, sensors, and basic circuits, in Greger R, Windhorst u (ed.), Comprehensive Human Physiology: From Cellular Mechanisms to Integration, Springer, Berlin, Vol. 1, Ch. 49, 1996.
24. Zenner HP, Hearing, in Greger R, Windhorst u (ed.), Comprehensive Human Physiology: From Cellular Mechanisms to Integration Greger R, Windhorst U (eds.), Springer, Berlin, Vol. 1, Ch. 35, 1996.
25. Arbib MA, érdi P, Szentágothai J, Neural Organization - Structure, Function, and Dynamics, The MIT Press, Cambridge, MA, pp. 120-127, 1998.
26. Wang DL, Emergent synchrony in locally coupled neural oscillators, IEEE Trans Neural Netw. 6:941-948, 1995.
27. Haykin S, Neural Networks - A Comprehensive Foundation, Prentice Hall, Upper Saddle River, NJ, pp. 678, 1999.
28. Slotnick B, Bodyak N, Odor discrimination and odor quality perception in rats with disruption of connections between the olfactory epithelium and olfactory bulbs, J Neurosci 22:4205-4216, 2002.
29. White J, Hamilton KA, Neff SR, Kauer JS, Emergent properties of odor information coding in a representational model of the salamander olfactory bulb, J Neurosci 12:1772-1780, 1992.
30. Davison AP, Feng J, Brown D, Dendrodendritic inhibition and simulated odor responses in a detailed olfactory bulb network model, J Neurophysiol 90:1921-1935, 2003.
31. Cooke KL, Grossman Z, Discrete delay, distributed delay and stability switches, J Math Anal Appl 86:592-627, 1982.
32. Freeman WJ, The physiology of perception, Sci Am 264(2):78-85, 1991.
33. Korsching S, Olfactory maps and odor images, Curr Opin Neurobiol 12:387-392, 2002.
34. Lledo PM, Gheusi G, Vincent JD, Information processing in the mammalian olfactory system, Physiol Rev 85:281-317, 2005.
35. Friedman D, Strowbridge BW, Both electrical and chemical synapses mediate fast network oscillations in the olfactory bulb, J Neurophysiol 89:2601-2610, 2003.
36. Kay LM, Two species of gamma oscillations in the olfactory bulb: dependence on behavioral state and synaptic interactions, J Integr Neurosci 2:31-44, 2003.
37. Fletcher ML, Smith AM, Best AR, Wilson DA, High-frequency oscillations are not necessary for simple olfactory discriminations in young rats, J Neurosci 25:792-798, 2005.
38. Gray CM, Skinner JE, Centrifugal regulation of neuronal activity in the olfactory bulb of the waking rabbit as revealed by reversible cryogenic blockade, Exp Brain Res 69:378-836, 1988.