Dynamical Systems in Neuroscience:

446 ReferencesGuckenheimer J. (1975) Isochrons and Phaseless Sets. Journal of Mathematical Biology, 1:259–273.Guevara M.R. and Glass L. (1982) Phase locking, periodic doubling bifurcations and chaos ina mathematical model of a periodically driven oscillator: a theory for the entrainment ofbiological oscillators and the generation of cardiac dysrhythmias. Math. Biol. 14: 1-23.Guttman R., Lewis S., Rinzel J. (1980) Control of repetitive firing in squid axon membrane asa model for a neuroneoscillator. J. Physiology. 305: 377-395.Hansel D., Mato G., and Meunier C. (1995) Synchrony in excitatory neural networks. NeuralComputations 7:307–335.Hansel D. and Mato G. (2003) Asynchronous States and the Emergence of Synchrony in LargeNetworks of Interacting Excitatory and Inhibitory Neurons. Neural Computation, 15:1–56.Hansel D., Mato G., Meunier C., and Neltner L. (1998) On Numerical Simulations of Integrateand-FireNeural Networks. Neural Computation, 10:467–483.Harris-Warrick R.M. and Flamm R.E. (1987) Multiple mechanisms of bursting in a conditionalbursting neuron. J. Neurosci., 7:2113–2128Hastings J.W. and Sweeney B.M. (1958) A persistent diurnal rhythms of luminescence inGonyaulax polyedra. Biol. Bull. 115:440-458.Hausser M., Spruston N., and Stuart G.J. (2000) Diversity and Dynamics of Dendritic Signaling.Science, 290:739–744Hausser M. and Mel B. (2003) Dendrites: bug or feature? Current Opinion in Neurobiology,13:372–383Heyward P., Ennis M., Keller A., and Shipley M.T. (2001) Membrane Bistability in OlfactoryBulb Mitral Cells The Journal of Neuroscience, 21:5311–5320Hille B. (2001) Ion Channels of Excitable Membranes. (2nd edition) Sinauer, Sunderland, MA.Hindmarsh J.L. and Rose R.M. (1982) A model of the nerve impulse using two first-orderdifferential equations. Nature 296:162–164Hines M.A. (1989) Program for simulation of nerve equations with branching geometries. Int JBiomed Comput 24:55–68.Hodgkin A.L. (1948) The local electric changes associated with repetitive action in a nonmedulatedaxon. Journal of Physiology 107:165–181.Hodgkin A.L. and Huxley A.F. (1952) A quantitative description of membrane current andapplication to conduction and excitation in nerve. Journal Physiol., 117:500–544.Holden L. and Erneux T. (1993a) Slow passage through a Hopf bifurcation: form oscillatory tosteady state solutions. SIAM Journal on Applied Mathematics 53:1045–1058Holden L. and Erneux T. (1993b) Understanding bursting oscillations as periodic slow passagesthrough bifurcation and limit points. J. Math. Biol. 31:351–365Hopf E. (1942) Abzweigung einer periodischen Losung von einer stationaren Losung eines Differetialsystems.Ber. Math.-Phys. Kl. Sachs, Aca. Wiss. Leipzig, 94:1–22.Hoppensteadt F.C. (1997) An Introduction to the Mathematics of Neurons. Second edition:Modeling in the Frequency Domain. Cambridge Univ. Press, Cambridge, U. K.