Date :

 7-8 October 2005

Place :

 Room 312, Department of Physics, National Taiwan University

 National Center for Theoretical Sciences (Critical Phenomena and Complex Systems focus group)

 Institute of Physics of Academia Sinica (Taipei)

 Miss Chia-Chi Liu (Secretary, Physics Division, NCTS)
 Tel:(886)-2-33665566; Fax:(886)-2-33665565; E-mail: ccliu@phys.ntu.edu.tw

          Speaker :　

Prof. Chi-Ming Chen

Department of Physics, National Taiwan Normal University, Taipei, TAIWAN

cchen@phy.ntnu.edu.tw

Dr. Syamal Dana

Instrument Division Indian Institute of Chemical Biology, Calcutta 32, INDIA

sdana_ecsu@yahoo.com

The usual phase synchronization shows that frequency mismatch of two or more coupled oscillators decreases monotonically with coupling. The oscillators finally rotate with a common frequency above a threshold coupling. On the contrary, anomalous transition to phase synchronization shows first an unusual increase in frequency difference of the coupled oscillators with coupling, with a maximal difference at intermediate coupling levels, before the onset of usual phase synchronization via monotonic decrease in frequency difference for larger coupling. Anomalous phase synchronization originates in the nonisochronicity of oscillations and arises when the nonisochronicity covaries with the natural frequency of the oscillation. Nonisochronicity as a shear of phase flow induces an amplitude dependence of the natural frequency of an oscillator. APS is established both theoretically and analytically as a universal phenomenon, which may be observed in any coupled system, e.g. with local and global coupling, and it appears as well in only two interacting systems. The exact condition for APS in any system can be derived with an appropriate choice of system parameters, when two or more parameters of a system are functionally dependent. We also observed anomalous transitions to both in-phase and anti-phase synchronization in electronic circuit experiments with Chua oscillators.

We observed homoclinic chaos of the Shil’nikov type in a single asymmetry-induced Chua's oscillator. The asymmetry is introduced in the circuit by forcing a DC voltage. The asymmetry plays a crucial role in the related homoclinic bifurcations. For selected strength of asymmetry when a system parameter is controlled, we observed that a large amplitude limit cycle tends to a homoclinic orbit and then moves to a bursting regime. This bursting is cycle-cycle type that shows repeated switching between large amplitude limit cycle and small amplitude saddle cycle. In this bursting regime we also observed periodic mixed mode oscillations interspersed by chaotic states. Finally, the dynamics moves to homoclinic chaos of the Shil’nikov type with a control parameter. Interesting point to note that we observed similar bursting and homoclinic chaos in two weakly coupled Chua oscillators when one of the coupled oscillators is in excitable state. The excitable oscillator, in fact, induces asymmetry in the firing or limit cycle oscillator via coupling where the coupling controls the strength of asymmetry. The results have relevance to investigations on dynamics of coupled system, in general, how one excitable system may influence the dynamics of a firing oscillator in close neighborhood.

We report neuron-like spiking and bursting in resistive-capacitive-inductive shunted Josephson junction (RCLSJ) model. Spiking oscillations namely, regular spiking (RS), intrinsically bursting (IB) and fast spiking (FS) as usually seen in rat's motor cortex are observed in a single junction under external DC bias. The spiking junction voltage is amplitude modulated as well as frequency modulated when forced by weak sinusoidal signal of frequency much lower than the junction resonant frequency. For stronger forcing, bursting oscillations are observed. The junction also shows autonomous bursting in the high inductive regime.

Multiscroll attractors are observed in two undirectionally coupled double scroll type oscillators like Chua's circuit and Lorenz system. In reality, when double scroll chaos of one oscillator is forced into a similar oscillator but in excitable state, we observed multi-scroll attractors in an intermittency regime of weaker coupling. We present our results of numerical as well as experimental studies in both coupled Chua's circuit and Lorenz system.
　

Gluing bifurcation is recently observed in many experimental systems and even its signatures are observed in natural system like cardiac arrhythmia. We report gluing bifurcation in reflection symmetric Chua Oscillator using both experimental and numerical approaches. Numerical simulation shows that one may observe gluing of a pair of homoclinic orbits at a critical value of control parameter. The emergence of gluing point is shown in a period parameter bifurcation diagram. Regions of gluing are demarcated in two-parameter bifurcation of the Chua oscillator. In experiment, due to the presence of noise and component mismatch, the system can no longer be considered perfectly reflection symmetric. However, we observed imperfect gluing bifurcation when a pair of periodic orbits tends to homoclinicity with a control parameter but finally breaks into a large homoclinic orbit. 

Mr. Maksim Kouza

Institute of Physics, Polish Academy of Sciences, POLAND

kouza@ifpan.edu.pl

The folding of the hbSBD domain in BCKD complex is studied experimentally by circular dichroism technique and numerically using the off-lattice coarse-grained Go model and Langevin dynamics. Both experimental and simulation results suggest that hbSBD domain is a two-state folder.
The dependence of cooperativity of the thermal denaturation transition on the number of aminoacids, N, is analyzed using available experimental data and simulation of Go models. It is shown that the structural cooperativity scales with N as a power low with the universal exponent. The folding rates are found to be strongly correlated with N.