scholarly journals Collective phase synchronization in locally coupled limit-cycle oscillators

2004 ◽  
Vol 70 (4) ◽  
Author(s):  
H. Hong ◽  
Hyunggyu Park ◽  
M. Y. Choi
Keyword(s):  
Limit Cycle ◽  
Phase Synchronization

DYNAMICS OF COLLECTIVE MULTI-STABILITY IN MODELS OF MULTI-UNIT NEURONAL SYSTEMS

2014 ◽  
Vol 24 (02) ◽  
pp. 1430004 ◽  
Author(s):  
MARC KOPPERT ◽  
STILIYAN KALITZIN ◽  
DEMETRIOS VELIS ◽  
FERNANDO LOPES DA SILVA ◽  
MAX A. VIERGEVER
Keyword(s):  
Limit Cycle ◽  
Analytical Model ◽  
Computational Models ◽  
Phase Synchronization ◽  
Neuronal Model ◽  
Model Type ◽  
Single Output ◽  
Patterns Of Behavior ◽  
Set Up ◽  
Neuronal Systems

In this study, we investigate the correspondence between dynamic patterns of behavior in two types of computational models of neuronal activity. The first model type is the realistic neuronal model; the second model type is the phenomenological or analytical model. In the simplest model set-up of two interconnected units, we define a parameter space for both types of systems where their behavior is similar. Next we expand the analytical model to two sets of 90 fully interconnected units with some overlap, which can display multi-stable behavior. This system can be in three classes of states: (i) a class consisting of a single resting state, where all units of a set are in steady state, (ii) a class consisting of multiple preserving states, where subsets of the units of a set participate in limit cycle, and (iii) a class consisting of a single saturated state, where all units of a set are recruited in a global limit cycle. In the third and final part of the work, we demonstrate that phase synchronization of units can be detected by a single output unit.

CHAOTIC PHASE SYNCHRONIZATION AND ITS BREAKDOWN - MAPPING MODEL AND CRITICAL DYNAMICS

2007 ◽  
Vol 21 (23n24) ◽  
pp. 3909-3917 ◽  
Author(s):  
HIROKAZU FUJISAKA ◽  
NAOFUMI TSUKAMOTO ◽  
SATOKI UCHIYAMA
Keyword(s):  
Limit Cycle ◽  
Phase Synchronization ◽  
Critical Dynamics ◽  
Coupled Oscillator ◽  
Chaotic Oscillators ◽  
Mapping Model ◽  
Phase Map ◽  
Coupled Oscillator Systems

In the present paper, we briefly discuss the construction of mapping model of coupled oscillator systems for limit-cycle oscillators and chaotic oscillators. A comparison of the proposed mapping model and other models, i.e., the Ikeda map and the phase map model is made. Furthermore, the critical dynamics associated with the breakdown of chaotic phase synchronization based on the present mapping model is discussed.

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