PHASE SYNCHRONIZATIONS: TRANSITIONS FROM HIGH- TO LOW-DIMENSIONAL TORI THROUGH CHAOS

2000 ◽  
Vol 10 (10) ◽  
pp. 2399-2414 ◽  
Author(s):  
BAMBI HU ◽  
ZHIGANG ZHENG
Keyword(s):  
Limit Cycles ◽  
Chaotic Dynamics ◽  
Statistical Approach ◽  
Phase Synchronization ◽  
Nonequilibrium Phase Transition ◽  
Recent Developments ◽  
Low Dimensional ◽  
Intermittent Chaos ◽  
Ordered State ◽  
Statistical Viewpoint

Phase synchronized entrainment of coupled nonidentical limit cycles and chaotic oscillators is a generic phenomenon in complicated and chaotic dynamics. Recent developments in phase synchronization are reviewed. Two approaches: The statistical approach and the dynamical approach are proposed. From a statistical viewpoint, phase entrainment exhibits a nonequilibrium phase transition from the disordered state to the ordered state. Dynamically, phase synchronization among oscillators shows a tree-like bifurcation and a number of clustered states are experienced. The route from partial to complete phase synchronization for coupled limit cycles is identified as a cascade of transitions from high- to low-dimensional tori (quasiperiodicity) interrupted by intermittent chaos. For coupled periodic oscillators, desynchronization-induced chaos originates from the mixing of intermittent ON–OFF duration time scales. For coupled chaotic cases, the route to phase entrainment is identified as transitions from high- to low-dimensional chaos.

Charge-Ordered State and Low-Dimensional Magnetic Fluctuations in Yb5Ge4 Single Crystal

2021 ◽  
Vol 90 (4) ◽  
pp. 044703
Author(s):  
Shinji Michimura ◽  
Masashi Kosaka ◽  
Ayumi Machida ◽  
Ryosuke Numakura ◽  
Ryosuke Iizuka ◽  
...  
Keyword(s):  
Single Crystal ◽  
Magnetic Fluctuations ◽  
Low Dimensional ◽  
Ordered State

Rb2CaCu6(PO4)4O2, a novel oxophosphate with a shchurovskyite-type topology: synthesis, structure, magnetic properties and crystal chemistry of rubidium copper phosphates

2019 ◽  
Vol 75 (5) ◽  
pp. 903-913
Author(s):  
Sergey M. Aksenov ◽  
Elena Yu. Borovikova ◽  
Vladimir S. Mironov ◽  
Natalia A. Yamnova ◽  
Anatoly S. Volkov ◽  
...  
Keyword(s):  
Multicomponent System ◽  
Exchange Interactions ◽  
Magnetic Behavior ◽  
Molar Ratio ◽  
Monoclinic Space Group ◽  
Antiferromagnetic Exchange ◽  
X Ray ◽  
Low Dimensional ◽  
Fierce Competition ◽  
Ordered State

Single crystals of Rb2CaCu6(PO4)4O2 were synthesized by a hydrothermal method in the multicomponent system CuCl2–Ca(OH)2–RbCl–B2O3–Rb3PO4. The synthesis was carried out in the temperature range from 690 to 700 K and at the general pressure of 480–500 atm [1 atm = 101.325 kPa] from the mixture in the molar ratio 2CuO:CaO:Rb2O:B2O3:P2O5. The crystals studied by single-crystal X-ray analysis were found to be monoclinic, space group C2, a = 16.8913 (4), b = 5.6406 (1), c = 8.3591 (3) Å, β = 93.919 (3)°, V = 794.57 (4) Å3. The crystal structure of Rb2CaCu6(PO4)4O2 is similar to that of shchurovskyite and dmisokolovite and is based upon a heteropolyhedral open framework formed by polar layers of copper polyhedra linked via isolated PO4 tetrahedra. The presence of well-isolated 2D heteropolyhedral layers in the title compound suggests low-dimensional magnetic behavior which is masked, however, by the fierce competition between multiple ferromagnetic and antiferromagnetic exchange interactions. At T C = 25 K, Rb2CaCu6(PO4)4O2 reaches a magnetically ordered state with large residual magnetization.

COOPERATIVE PHASE DYNAMICS IN COUPLED NEPHRONS

2001 ◽  
Vol 15 (23) ◽  
pp. 3079-3098 ◽  
Author(s):  
D. E. POSTNOV ◽  
O. V. SOSNOVTSEVA ◽  
E. MOSEKILDE ◽  
N.-H. HOLSTEIN-RATHLOU
Keyword(s):  
Chaotic Dynamics ◽  
Phase Synchronization ◽  
Functional Unit ◽  
Flow Regulation ◽  
Tubuloglomerular Feedback ◽  
Phase Dynamics ◽  
The Individual ◽  
Fast Oscillations ◽  
Coherent Behavior ◽  
Different Time Scales

The individual functional unit of the kidney (the nephron) displays oscillations in its pressure and flow regulation at two different time scales: Relatively fast oscillations associated with the myogenic dynamics of the afferent arteriole, and slower oscillations related with a delay in the tubuloglomerular feedback. Neighboring nephrons interact via vascularly propagated signals. We study the appearance of various forms of coherent behavior in a model of two such interacting nephrons. Among the observed phenomena are in-phase and anti-phase synchronization of chaotic dynamics, multistability, and partial phase synchronization in which the nephrons attain a state of chaotic phase synchronization with respect to their slow dynamics, but the fast dynamics remains desynchronized.

STIMULUS-INDUCED CHAOTIC SYNCHRONIZATION OF CHUA'S OSCILLATORS

2006 ◽  
Vol 16 (10) ◽  
pp. 2843-2853
Author(s):  
V. V. KLINSHOV ◽  
V. B. KAZANTSEV ◽  
V. I. NEKORKIN
Keyword(s):  
Initial Phase ◽  
Chaotic Dynamics ◽  
Phase Synchronization ◽  
Cluster Formation ◽  
Time Moment ◽  
Chaotic Oscillation ◽  
Single Pulse ◽  
Chaotic Synchronization ◽  
Phase Reset ◽  
Chaotic Oscillators

The problem of phase synchronization of Chua's chaotic oscillators is investigated. We consider Chua's circuit when it exhibits a chaotic attractor and apply a single pulse stimulus. It is shown that under certain conditions the system displays self-referential phase reset (SPR) phenomenon. This is a case when the reset phase of the chaotic oscillation is independent on the initial phase, hence on the time moment when the stimulus has been applied. In an ensemble of chaotic oscillators simultaneously stimulated, the SPR yields mutual phase coherence or synchronization between the units. We describe basic dynamical mechanisms of the effect and show how it can be used for controllable cluster formation and for the control of chaotic dynamics.

QFT, STRINGS AND LOW-DIMENSIONAL TOPOLOGY

2002 ◽  
Vol 17 (35) ◽  
pp. 2289-2295
Author(s):  
HU SEN
Keyword(s):  
Mirror Symmetry ◽  
Theoretical Physics ◽  
Yang Mills ◽  
Low Dimensional Topology ◽  
Witten Theory ◽  
Close Relationship ◽  
Jones Polynomials ◽  
Recent Developments ◽  
Low Dimensional ◽  
Chern Simons

In between the 80's and 90's we witnessed deep interactions between mathematics and theoretical physics, especially in the understanding of low-dimensional topology in terms of quantum field theory. For example, Jones polynomials (Chern–Simons–Witten theory), Donaldson and Seiberg–Witten invariants (SUSY Yang–Mills theory) and mirror symmetry (T duality in strings) are all naturally understood in terms of QFT and strings. Recent developments indicate a close relationship between gauge theory and gravity theory both in physics and in low-dimensional topology. We shall survey these developments and report some of our work. We shall also find that the keys to connect geometric and physical objects are through symmetry and quantization.

UNIVERSALITY OF FIRST AND SECOND ORDER PHASE TRANSITION IN SOLAR ACTIVITY: EVIDENCE FOR NONEXTENSIVE TSALLIS STATISTICS

2012 ◽  
Vol 22 (09) ◽  
pp. 1250209 ◽  
Author(s):  
L. P. KARAKATSANIS ◽  
G. P. PAVLOS ◽  
D. S. SFIRIS
Keyword(s):  
Phase Transition ◽  
Solar Flare ◽  
Transition Process ◽  
High Dimensional ◽  
Nonequilibrium Phase Transition ◽  
Intermittent Turbulence ◽  
Chaotic State ◽  
Phase Transition Process ◽  
Low Dimensional ◽  
Q Values

In this work, we present the coexistence of self-organized criticality (SOC) and low-dimensional chaos at solar activity with results obtained by using the intermittent turbulence theory, the nonextensive q-statistics of Tsallis as well as the singular value decomposition analysis. Particularly, we show the independent dynamics of sunspot system related to the convection zone of sun and the solar flare system related to the lower solar atmosphere. However, both systems reveal nonequilibrium phase transition process from a high-dimensional intermittent turbulence state with SOC profile to a low-dimensional and chaotic intermittent turbulence state. The high-dimensional SOC state in both dynamical systems underlying the sunspot and solar flare signal is related with low q-values and low Flatness values (F) while the low-dimensional chaotic state is related with higher q-values and Flatness F-values. The higher q- and F-values reveal strong character of long-range correlations corresponding to system-wide global process while the lower q- and F-values reveal scale invariant local avalanche process. Also, the high-dimensional SOC state corresponds to second order nonequilibrium critical phase transition process while the low-dimensional chaotic state corresponds to first order nonequilibrium phase transition process. Finally, for both dynamics underlying sunspot index and solar flare, at both states of phase transition process, the multiscale and multifractal character was found to exist but with different profile or strength.

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