Pulse coupled oscillators and the phase resetting curve.
Limit cycle oscillators that are coupled in a pulsatile manner are referred to as pulse coupled oscillators. In these oscillators, the interactions take the form of brief pulses such that the effect of one input dies out before the next is received. A phase resetting curve (PRC) keeps track of how much an input advances or delays the next spike in an oscillatory neuron depending upon where in the cycle the input is applied. PRCs can be used to predict phase locking in networks of pulse coupled oscillators. In some studies of pulse coupled oscillators, a specific form is assumed for the interactions between oscillators, but a more general approach is to formulate the problem assuming a PRC that is generated using a perturbation that approximates the input received in the real biological network. In general, this approach requires that circuit architecture and a specific firing pattern be assumed. This allows the construction of discrete maps from one event to the next. The fixed points of these maps correspond to periodic firing modes and are easier to locate and analyze for stability compared to locating and analyzing periodic modes in the original network directly. Alternatively, maps based on the PRC have been constructed that do not presuppose a firing order. Specific circuits that have been analyzed under the assumption of pulsatile coupling include one to one lockings in a periodically forced oscillator or an oscillator forced at a fixed delay after a threshold event, two bidirectionally coupled oscillators with and without delays, a unidirectional N-ring of oscillators, and N all-to-all networks.
Canavier
Carmen C
CC
Neuroscience Center of Excellence, LSU Health Sciences Center, New Orleans, LA 70112, USA.
Achuthan
Srisairam
S
D000200:Action Potentials / Q000502:physiology; D000465:Algorithms; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology; D009474:Neurons / Q000502:physiology*
Science. 1964 Jul 3;145(3627):61-3
14162696
Curr Biol. 2004 May 4;14(9):796-800
15120072
Biophys J. 2009 Jul 8;97(1):59-73
19580744
J Neurosci. 2003 Jul 16;23(15):6280-94
12867513
J Neurophysiol. 2005 Mar;93(3):1197-208
15525802
J Neurosci. 2007 Feb 21;27(8):2058-73
17314301
Nat Neurosci. 2001 Dec;4(12):1259-64
11694886
Neuron. 2006 Oct 5;52(1):155-68
17015233
J Theor Biol. 1967 Jul;16(1):15-42
6035757
Trends Neurosci. 2007 Jul;30(7):357-64
17532060
Nature. 2010 Apr 8;464(7290):903-7
20336071
Int J Neural Syst. 2009 Jun;19(3):149-56
19575505
J Neurophysiol. 2005 Aug;94(2):1623-35
15829595
Trends Neurosci. 2004 Apr;27(4):218-24
15046881
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Dec;76(6 Pt 1):061912
18233874
J Physiol. 1948 Mar 15;107(2):165-81
16991796
Phys Rev Lett. 2002 Dec 16;89(25):258701
12484926
J Neurosci. 1996 Oct 15;16(20):6402-13
8815919
Biophys J. 2004 Oct;87(4):2283-98
15454430
J Comput Neurosci. 2008 Feb;24(1):37-55
17577651
Biol Cybern. 1997 Dec;77(6):367-80
9433752
J Comput Neurosci. 2010 Apr;28(2):305-21
20135213
Proc Natl Acad Sci U S A. 2003 Jun 24;100(13):7931-6
12792019
Prog Brain Res. 1994;102:383-94
7800828
Neural Comput. 2006 Nov;18(11):2617-50
16999573
Trends Neurosci. 2007 Jul;30(7):350-6
17544519
IEEE Trans Biomed Eng. 2004 Feb;51(2):205-18
14765693
Phys Rev Lett. 1996 Mar 4;76(10):1755-1758
10060509
J Neurophysiol. 2009 Jul;102(1):69-84
19357337
J Neural Eng. 2009 Dec;6(6):066003
19837998
Phys Rev Lett. 1995 Feb 27;74(9):1570-1573
10059062
Neural Comput. 2001 Jun;13(6):1285-310
11387047
Nature. 1999 Feb 4;397(6718):430-3
9989408
Trends Neurosci. 1993 Oct;16(10):389-94
7504352
Biol Cybern. 1999 Feb;80(2):87-102
21547616
Physiol Behav. 2002 Dec;77(4-5):629-33
12527010
Nat Rev Neurosci. 2005 Jun;6(6):477-83
15928717
J Neurophysiol. 2009 Jul;102(1):387-98
19420126
J Neurophysiol. 1994 Sep;72(3):1109-26
7807198
Neuroscience. 2009 Sep 1;162(3):797-804
19393291
J Neurophysiol. 1993 Mar;69(3):992-5
8463821
J Comput Neurosci. 2003 Jul-Aug;15(1):71-90
12843696
J Neurophysiol. 2000 Aug;84(2):975-85
10938321
Biophys J. 1981 Jul;35(1):193-213
7260316
Biol Cybern. 1999 Jan;80(1):11-23
20809292
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2 Pt 1):021908
19792152
J Neurosci. 2009 Apr 22;29(16):5218-33
19386918
J Comput Neurosci. 2005 Jun;18(3):287-95
15830165
J Comput Neurosci. 2009 Apr;26(2):303-20
18690530
Q Rev Biol. 1988 Sep;63(3):265-89
3059390