A Bonhoeffer-van der Pol oscillator model of locked and non-locked behaviors of living pacemaker neurons

A recent investigation of the influence of periodic inhibitory trains on a crayfish pacemaker neuron showed not only well-known locked periodic responses but also intermittent, messy, and hopping responses. This communication studies the responses of the Bonhoeffer-van der Pol (BVP) model with self-sustained oscillation when exposed to periodic pulse trains inputs. The analysis is similar to that used in crayfish and reveals interesting features, both comparable and complementary to those seen in the living preparation.

[1]  Å. Edman,et al.  Transmembrane ion balance in slowly and rapidly adapting lobster stretch receptor neurones. , 1986, The Journal of physiology.

[2]  Leon Glass,et al.  Bistability, period doubling bifurcations and chaos in a periodically forced oscillator , 1982 .

[3]  Gonzalez,et al.  Phase locking, period doubling, and chaotic phenomena in externally driven excitable systems. , 1988, Physical review. A, General physics.

[4]  M. Kawato Transient and steady state phase response curves of limit cycle oscillators , 1982 .

[5]  Walter J. Karplus,et al.  Dynamics of synaptic integration , 2006, Annals of Biomedical Engineering.

[6]  S. W. Kuffler,et al.  SYNAPTIC INHIBITION IN AN ISOLATED NERVE CELL , 1955, The Journal of general physiology.

[7]  Michael Stiber,et al.  PERIODIC INHIBITION OF LIVING PACEMAKER NEURONS (I): LOCKED, INTERMITTENT, MESSY, AND HOPPING BEHAVIORS , 1991 .

[8]  R. FitzHugh Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[9]  Michael Stiber,et al.  Periodic Inhibition of Living Pacemaker Neurons (ii): Influences of Driver Rates and Transients and of Nondriven Postsynaptic Rates , 1991 .

[10]  G. P. Moore,et al.  PACEMAKER NEURONS: EFFECTS OF REGULARLY SPACED SYNAPTIC INPUT. , 1964, Science.

[11]  S. W. Kuffler,et al.  PROCESSES OF EXCITATION IN THE DENDRITES AND IN THE SOMA OF SINGLE ISOLATED SENSORY NERVE CELLS OF THE LOBSTER AND CRAYFISH , 1955, The Journal of general physiology.

[12]  K. Bonhoeffer ACTIVATION OF PASSIVE IRON AS A MODEL FOR THE EXCITATION OF NERVE , 1948, The Journal of general physiology.

[13]  J. Nagumo,et al.  On a response characteristic of a mathematical neuron model , 1972, Kybernetik.

[14]  A. Winfree Biological rhythms and the behavior of populations of coupled oscillators. , 1967, Journal of theoretical biology.

[15]  S Sato,et al.  Response characteristics of the BVP neuron model to periodic pulse inputs. , 1992, Mathematical biosciences.

[16]  G. P. Moore,et al.  Interspike interval fluctuations in aplysia pacemaker neurons. , 1966, Biophysical journal.

[17]  Diego L. González,et al.  Chaos in a Nonlinear Driven Oscillator with Exact Solution , 1983 .

[18]  S. Yoshizawa,et al.  An Active Pulse Transmission Line Simulating Nerve Axon , 1962, Proceedings of the IRE.

[19]  G. P. Moore,et al.  Pacemaker Neurons: Effects of Regularly Spaced Synaptic Input , 1964, Science.

[20]  J. P. Segundo,et al.  Presynaptic irregularity and pacemaker inhibition , 1981, Biological Cybernetics.

[21]  K Aihara,et al.  Periodic and non-periodic responses of a periodically forced Hodgkin-Huxley oscillator. , 1984, Journal of theoretical biology.

[22]  J. -F. Vibert,et al.  Examination with a computer of how parameters changes and variabilities influence a model of oscillator entrainment , 2004, Biological Cybernetics.

[23]  Leon D. Harmon,et al.  Studies with artificial neurons, I: properties and functions of an artificial neuron , 1961, Kybernetik.