TY - GEN
T1 - Bonhoeffer-van der Pol oscillator under pulse-train forcing
AU - Rabinovitch, Avindam
AU - Thieberger, R.
AU - Friedman, M.
PY - 1993/12/1
Y1 - 1993/12/1
N2 - We analyze the Bonhoeffer-van der Pol equations in a parameter range where no `overt' limit cycle exists, rather the dominating feature in phase space is a focus. Exciting the system by an external pulse, its response depends upon this pulse's size. For small pulses, a quick return to the focus occurs. For large pulses, extending beyond the separatrix, the orbits traverse along a `hidden' structure. This structure initially resembles a temporary limit cycle and then spirals into the focus. The response of the system to single excitations of different sizes at different points of the `hidden' structure is used to understand its response to a train of pulses of different periods. Thus, e.g. the boundaries of the phase- locking regions are easily calculated and the explanation of the appearance of `below threshold' responses for the pulse-train case becomes straightforward.
AB - We analyze the Bonhoeffer-van der Pol equations in a parameter range where no `overt' limit cycle exists, rather the dominating feature in phase space is a focus. Exciting the system by an external pulse, its response depends upon this pulse's size. For small pulses, a quick return to the focus occurs. For large pulses, extending beyond the separatrix, the orbits traverse along a `hidden' structure. This structure initially resembles a temporary limit cycle and then spirals into the focus. The response of the system to single excitations of different sizes at different points of the `hidden' structure is used to understand its response to a train of pulses of different periods. Thus, e.g. the boundaries of the phase- locking regions are easily calculated and the explanation of the appearance of `below threshold' responses for the pulse-train case becomes straightforward.
UR - http://www.scopus.com/inward/record.url?scp=0027804540&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:0027804540
SN - 0819412856
T3 - Proceedings of SPIE - The International Society for Optical Engineering
SP - 215
EP - 219
BT - Proceedings of SPIE - The International Society for Optical Engineering
A2 - Ditto, William L.
PB - Publ by Society of Photo-Optical Instrumentation Engineers
T2 - Chaos in Biology and Medicine
Y2 - 12 July 1993 through 13 July 1993
ER -