Analysis and control of discrete-time piecewise linear time-delay systems

2009 ◽  
Author(s):  
Mei-Jin Xu ◽  
Yan Zhao ◽  
Wei Deng
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Linear Time ◽  
Piecewise Linear ◽  
Delay Systems ◽  
Time Delay Systems ◽  
And Control

scholarly journals GLOBAL AND PARTIAL PHASE SYNCHRONIZATIONS IN ARRAYS OF PIECEWISE LINEAR TIME-DELAY SYSTEMS

2012 ◽  
Vol 22 (07) ◽  
pp. 1250178 ◽  
Author(s):  
R. SURESH ◽  
D. V. SENTHILKUMAR ◽  
M. LAKSHMANAN ◽  
J. KURTHS
Keyword(s):  
Time Delay ◽  
Boundary Conditions ◽  
Coupling Strength ◽  
Phase Synchronization ◽  
Linear Array ◽  
Linear Time ◽  
Piecewise Linear ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Partial Phase

In this paper, we report the phenomena of global and partial phase synchronizations in linear arrays of unidirectionally coupled piecewise linear time-delay systems. In particular, in a linear array with open end boundary conditions, global phase synchronization (GPS) is achieved by a sequential synchronization of local oscillators in the array as a function of the coupling strength (a second order transition). Several phase synchronized clusters are also formed during the transition to GPS at intermediate values of the coupling strength, as a prelude to full scale synchronization. On the other hand, in a linear array with closed end boundary conditions (ring topology), partial phase synchronization (PPS) is achieved by forming different groups of phase synchronized clusters above some threshold value of the coupling strength (a first order transition) where they continue to be in a stable PPS state. We confirm the occurrence of both global and partial phase synchronizations in two different piecewise linear time-delay systems using various qualitative and quantitative measures in three different frameworks, namely, using explicit phase, recurrence quantification analysis and the framework of localized sets.

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