Dynamical analysis of neural oscillators in an olfactory cortex model

IEEE Transactions on Neural Networks

Volumn 15, Issue 5, 2004, Pages 1053-1062

  Xu, Dongming ^a   Principe, José C ^a  

^a University of Florida   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; OSCILLATORS (ELECTRONIC); SENSORY PERCEPTION; STABILITY; VLSI CIRCUITS;

BIFURCATION ANALYSIS; NONLINEAR OSCILLATORS; OLFACTORY SYSTEM; STABILITY CONDITIONS;

NEURAL NETWORKS;

ACTION POTENTIAL; ANIMAL; ARTICLE; BIOLOGICAL MODEL; BIOLOGICAL RHYTHM; COMPUTER SIMULATION; HUMAN; NERVE CELL; NERVE TRACT; NONLINEAR SYSTEM; ODOR; OLFACTORY SYSTEM; PHYSIOLOGY; SYNAPTIC TRANSMISSION;

ACTION POTENTIALS; ANIMALS; BIOLOGICAL CLOCKS; COMPUTER SIMULATION; HUMANS; MODELS, NEUROLOGICAL; NEURAL PATHWAYS; NEURONS; NONLINEAR DYNAMICS; OLFACTORY PATHWAYS; SMELL; SYNAPTIC TRANSMISSION;

EID: 4644226686     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2004.832815     Document Type: Article

References (15)

1. W. Freeman, Mass Action in the Nervous System. New York: Academic, 1975.
2. J. Principe, V. Tavares, J. Harris, and W. Freeman, "Design and implementation of a biologically realistic olfactory cortex in analog VLSI," Proc. IEEE, vol. 89, no. 7, pp. 569-571, July 2001.
3. R. Llinas, 1 of the Vortex: From Neurons to Self. Cambridge, MA: MIT Press, 2001.
4. S. Kelso, Dynamic Patterns: The Self-Organization of Brain and Behavior. Cambridge, MA: MIT Press, 1995.
5. V. Tavares, "Design and implementation of a biologically realistic olfactory cortex model," Ph.D. dissertation, Univ. of Florida, Gainesville, FL, May 2001.
6. S. Grossberg, "Pattern learning by functional-differential neural networks with arbitrary path weights," in Delay and Functional Differential Equations and Their Applications, S. Schmitt, Ed. New York: Academic, 1972, pp. 121-160.
7. J. Hopfield, "Neurons with graded response have collective computational properties like those of two-state neurons," Proc. Nat. Acad. Sci., vol. 81, pp. 3088-3092, 1984.
8. D. Kaplan and L. Glass, Understanding Nonlinear Dynamics. New York: Springer-Verlag, 1995.
9. Y. Yao, W. Freeman, B. Burke, and Q. Yang, "Pattern recognition by a distributed neural network: an industrial application," Neural Netw., vol. 4, no. 1, pp. 103-121, 2001.
10. R. Kozma and W. Freeman, "Chaotic resonance-methods and applications for robust classification of noisy and variable patterns," Int. J. Bifurcation Chaos, vol. 11, no. 6, pp. 1607-1629, 2001.
11. W. Freeman and S. Jakubith, "Bifurcation analysis of continuous time dynamics of oscillatory neural networks," in Brain Theory-Spatio-Temporal Aspects of Brain Function, A. Aertsen and W. von Seelen, Eds. Amsterdam, The Netherlands: Elsevier, 1993, pp. 183-208.
12. F. Hoppensteadt, Analysis and Simulation of Chaotic Systems, 2nd ed. New York: Springer-Verlag, 2000.
13. Y. Kuznetsov, L. Kuznetsov, and J. Marsden, Elements of Applied Bifurcation Theory, 2nd ed. New York: Springer-Verlag, 1998.
14. W. D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations, 2nd. Oxford, U.K.: Clarendon, 1987.
15. J. Palis Jr. and W. de Melo, Geometric Theory of Dynamical Systems. New York: Springer-Verlag, 1982.