Exploring the route to measure synchronization in non-linearly coupled Hamiltonian systems

The transition to measure synchronization in two coupled φ4 equations are investigated numerically both for quasiperiodic and chaotic cases. Quantities like the bare energy and phase difference are employed to study the underlying behaviors during this process. For transition between quasiperiodic states, the distribution of phase difference tends to concentrate at large angles before measure synchronization, and is confined to within a certain range after measure synchronization. For transition between quasiperiodicity and chaos, phase locking is not achieved and a random-walk-like behavior of the phase difference is found in the measure synchronized region. The scaling relationship of the phase distribution and the behavior of the bare energy are also discussed.

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MEASURE SYNCHRONIZATION IN A COUPLED HAMILTONIAN SYSTEM ASSOCIATED WITH NONLINEAR SCHRÖDINGER EQUATION

Modern Physics Letters B ◽

10.1142/s0217984905008748 ◽

2005 ◽

Vol 19 (15) ◽

pp. 737-742 ◽

Cited By ~ 6

Author(s):

U. E. VINCENT ◽

A. N. NJAH ◽

O. AKINLADE

Keyword(s):

Phase Space ◽

Hamiltonian System ◽

Invariant Measure ◽

Schrödinger Equation ◽

Hamiltonian Systems ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Measure Synchronization

We present preliminary numerical findings concerning measure synchronization in a pair of coupled Nonlinear Hamiltonian Systems (NLHS) derived from a Nonlinear Schrödinger Equation (NLSE). The dynamics of the two coupled NLHS were found to exhibit a transition to coherent invariant measure; their orbits sharing the same phase space as the coupling strength is increased. Transitions from quasiperiodicity (QP) measure desynchronization to QP measure synchronization and QP measure desynchronization to chaotic (CH) measure synchronization were observed.

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Mechanism of measure synchronization in coupled Hamiltonian systems

Acta Physica Sinica ◽

10.7498/aps.59.3763 ◽

2010 ◽

Vol 59 (6) ◽

pp. 3763

Author(s):

Tian Jing ◽

Qiu Hai-Bo ◽

Chen Yong

Keyword(s):

Hamiltonian Systems ◽

Measure Synchronization

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PARTIAL MEASURE SYNCHRONIZATION IN HAMILTONIAN SYSTEMS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127402004978 ◽

2002 ◽

Vol 12 (05) ◽

pp. 1141-1148 ◽

Cited By ~ 8

Author(s):

XINGANG WANG ◽

HAIHONG LI ◽

KAI HU ◽

GANG HU

Keyword(s):

Hamiltonian Systems ◽

Coupling Strength ◽

Particle Energy ◽

Complete Synchronization ◽

Partial Synchronization ◽

Measure Synchronization

Partial synchronization in Hamiltonian systems is investigated based on the concept of measure-synchronization. The classical φ4 model is used for the investigation. A macroscopic observable of long-term average of particle energy is computed to describe transitions between desynchronization, different partial synchronization, and complete synchronization structures. It is found that, prior to the entire synchronization of all oscillators, partial measure-synchronization for some clusters of oscillators is stable within certain regions. Moreover, transition from quasiperiodicity to chaos is observed to be associated with the measure-synchronization as the coupling strength is increased.

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Measure Synchronization of High-Cycle Islets in Coupled Hamiltonian Systems

Chinese Physics Letters ◽

10.1088/0256-307x/21/11/015 ◽

2004 ◽

Vol 21 (11) ◽

pp. 2128-2131 ◽

Cited By ~ 5

Author(s):

Chen Shao-Ying ◽

Wang Guang-Rui ◽

Chen Shi-Gang

Keyword(s):

Hamiltonian Systems ◽

Measure Synchronization

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Measure Synchronization in Coupled Hamiltonian Systems

Physical Review Letters ◽

10.1103/physrevlett.83.2179 ◽

1999 ◽

Vol 83 (11) ◽

pp. 2179-2182 ◽

Cited By ~ 55

Author(s):

Alan Hampton ◽

Damián H. Zanette

Keyword(s):

Hamiltonian Systems ◽

Measure Synchronization

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POINCARÉ SECTION ANALYSIS TO MEASURE SYNCHRONIZATION IN COUPLED HAMILTONIAN SYSTEMS

Modern Physics Letters B ◽

10.1142/s021798491350036x ◽

2013 ◽

Vol 27 (05) ◽

pp. 1350036 ◽

Cited By ~ 5

Author(s):

JING TIAN ◽

HAIBO QIU ◽

ZICHEN CHEN ◽

YONG CHEN

Keyword(s):

Hamiltonian Systems ◽

Underlying Mechanism ◽

Poincaré Section ◽

Analysis Method ◽

Poincare Section ◽

Section Technique ◽

Measure Synchronization ◽

General Explanation ◽

Section Analysis ◽

General Method

As a novel synchronization phenomenon, measure synchronization (MS) in Hamiltonian systems is characterized by a commonly shared phase space that has invariant measure. Although there has been some discussions of the underlying mechanism, a general explanation of MS is still lacking. In this paper, we reveal the essence of MS by using Poincaré section analysis. A two coupled Bosonic Josephson junction model is employed to perform the analysis as an illustration. It is shown that coupled Hamiltonian systems exhibit separatrix crossing behavior at quasiperiodic MS transition. Moreover, using this analysis method we find that chaotic MS is the result of separatrix chaos. It is concluded that the Poincaré section technique is a general method to explain MS, and the direct correspondence between separatrix behavior and the MS transition is a universal property in coupled Hamiltonian systems.

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