Bonhoeffer-van der Pol oscillator under pulse-train forcing

Avindam Rabinovitch; R. Thieberger; Menahem Friedman

doi:10.1117/12.162714

5 November 1993 Bonhoeffer-van der Pol oscillator under pulse-train forcing

Avindam Rabinovitch, R. Thieberger, Menahem Friedman

Proceedings Volume 2036, Chaos in Biology and Medicine; (1993) https://doi.org/10.1117/12.162714
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States

Abstract

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.

Citation Download Citation

Avindam Rabinovitch, R. Thieberger, and Menahem Friedman "Bonhoeffer-van der Pol oscillator under pulse-train forcing", Proc. SPIE 2036, Chaos in Biology and Medicine, (5 November 1993); https://doi.org/10.1117/12.162714

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available