PMID- 26565311
OWN - NLM
STAT- MEDLINE
DCOM- 20160822
LR  - 20151114
IS  - 1550-2376 (Electronic)
IS  - 1539-3755 (Linking)
VI  - 92
IP  - 4
DP  - 2015 Oct
TI  - Emergence and combinatorial accumulation of jittering regimes in spiking 
      oscillators with delayed feedback.
PG  - 042914
LID - 10.1103/PhysRevE.92.042914 [doi]
AB  - Interaction via pulses is common in many natural systems, especially neuronal. In 
      this article we study one of the simplest possible systems with pulse 
      interaction: a phase oscillator with delayed pulsatile feedback. When the 
      oscillator reaches a specific state, it emits a pulse, which returns after 
      propagating through a delay line. The impact of an incoming pulse is described by 
      the oscillator's phase reset curve (PRC). In such a system we discover an 
      unexpected phenomenon: for a sufficiently steep slope of the PRC, a periodic 
      regular spiking solution bifurcates with several multipliers crossing the unit 
      circle at the same parameter value. The number of such critical multipliers 
      increases linearly with the delay and thus may be arbitrary large. This 
      bifurcation is accompanied by the emergence of numerous "jittering" regimes with 
      nonequal interspike intervals (ISIs). Each of these regimes corresponds to a 
      periodic solution of the system with a period roughly proportional to the delay. 
      The number of different "jittering" solutions emerging at the bifurcation point 
      increases exponentially with the delay. We describe the combinatorial mechanism 
      that underlies the emergence of such a variety of solutions. In particular, we 
      show how a periodic solution exhibiting several distinct ISIs can imply the 
      existence of multiple other solutions obtained by rearranging of these ISIs. We 
      show that the theoretical results for phase oscillators accurately predict the 
      behavior of an experimentally implemented electronic oscillator with pulsatile 
      feedback.
FAU - Klinshov, Vladimir
AU  - Klinshov V
AD  - Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov 
      Street, 603950, Nizhny Novgorod, Russia.
FAU - Lucken, Leonhard
AU  - Lucken L
AD  - Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 
      10117, Berlin, Germany.
FAU - Shchapin, Dmitry
AU  - Shchapin D
AD  - Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov 
      Street, 603950, Nizhny Novgorod, Russia.
FAU - Nekorkin, Vladimir
AU  - Nekorkin V
AD  - Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov 
      Street, 603950, Nizhny Novgorod, Russia.
AD  - University of Nizhny Novgorod, 23 Prospekt Gagarina, 603950, Nizhny Novgorod, 
      Russia.
FAU - Yanchuk, Serhiy
AU  - Yanchuk S
AD  - Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 
      10117, Berlin, Germany.
LA  - eng
PT  - Journal Article
PT  - Research Support, Non-U.S. Gov't
DEP - 20151014
PL  - United States
TA  - Phys Rev E Stat Nonlin Soft Matter Phys
JT  - Physical review. E, Statistical, nonlinear, and soft matter physics
JID - 101136452
SB  - IM
MH  - *Feedback, Physiological
MH  - Linear Models
MH  - Models, Neurological
MH  - Neurons/*cytology
EDAT- 2015/11/14 06:00
MHDA- 2016/08/23 06:00
CRDT- 2015/11/14 06:00
PHST- 2015/06/11 00:00 [received]
PHST- 2015/11/14 06:00 [entrez]
PHST- 2015/11/14 06:00 [pubmed]
PHST- 2016/08/23 06:00 [medline]
AID - 10.1103/PhysRevE.92.042914 [doi]
PST - ppublish
SO  - Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042914. doi: 
      10.1103/PhysRevE.92.042914. Epub 2015 Oct 14.