System-Size Effects on the Collective Dynamics of Cell Populations with Global Coupling

Phase-transitionlike behavior is found to occur in globally coupled systems of finite number of elements, and its theoretical explanation is provided. The system studied is a population of globally pulse-coupled integrate-and-fire cells subject to small additive noise. As the population size is changed, the system shows a phase-transitionlike behavior. That is, there exits a well-defined critical system size above which the system stays in a monostable state with high-frequency activity while below which a new phase characterized by alternation of high- and low frequency activities appears. The mean field motion obeys a stochastic process with state-dependent noise, and the above phenomenon can be interpreted as a noise-induced transition characteristic to such processes. Coexistence of high- and low frequency activities observed in finite size systems is reported by N. Cohen, Y. Soen and E. Braun[Physica A249, 600 (1998)] in the experiments of cultivated heart cells. The present report gives the first qualitative interpretation of their experimental results

Anharmonic resonances with recursive delay feedback

We consider application of the multiple time delayed feedback for control of anharmonic (nonlinear) oscillators subject to noise. In contrast to the case of a single delay feedback, the multiple one exhibits resonances between feedback and nonlinear harmonics, leading to a resonantly strong or weak oscillation coherence even for a small anharmonicity. Analytical results are confirmed numerically for van der Pol and van der Pol-Duffing oscillators. Highlights: > We construct general theory of noisy limit-cycle oscillators with linear feedback. > We focus on coherence and "reliability" of oscillators. > For recursive delay feedback control the theory shows importance of anharmonicity. > Anharmonic resonances are studied both numerically and analytically.Comment: 6 pages, 4 figures, +Maple program and its pdf-print, submitted to Physics Letters

Dynamics of Limit Cycle Oscillator Subject to General Noise

The phase description is a powerful tool for analyzing noisy limit cycle oscillators. The method, however, has found only limited applications so far, because the present theory is applicable only to the Gaussian noise while noise in the real world often has non-Gaussian statistics. Here, we provide the phase reduction for limit cycle oscillators subject to general, colored and non-Gaussian, noise including heavy-tailed noise. We derive quantifiers like mean frequency, diffusion constant, and the Lyapunov exponent to confirm consistency of the result. Applying our results, we additionally study a resonance between the phase and noise.Comment: main paper: 4 pages, 2 figure; auxiliary material: 5-7 pages of the document, 1 figur

Implementation of analytical Hartree-Fock gradients for periodic systems

We describe the implementation of analytical Hartree-Fock gradients for periodic systems in the code CRYSTAL, emphasizing the technical aspects of this task. The code is now capable of calculating analytical derivatives with respect to nuclear coordinates for systems periodic in 0, 1, 2 and 3 dimensions (i.e. molecules, polymers, slabs and solids). Both closed-shell restricted and unrestricted Hartree-Fock gradients have been implemented. A comparison with numerical derivatives shows that the forces are highly accurate.Comment: accepted by Comp. Phys. Com

Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators

We study synchronization properties of general uncoupled limit-cycle oscillators driven by common and independent Gaussian white noises. Using phase reduction and averaging methods, we analytically derive the stationary distribution of the phase difference between oscillators for weak noise intensity. We demonstrate that in addition to synchronization, clustering, or more generally coherence, always results from arbitrary initial conditions, irrespective of the details of the oscillators.Comment: 6 pages, 2 figure

A Wannier-function-based ab initio Hartree-Fock study of polyethylene

In the present letter, we report the extension of our Wannier-function-based ab initio Hartree-Fock approach---meant originally for three-dimensional crystalline insulators---to deal with quasi-one-dimensional periodic systems such as polymers. The system studied is all-transoid polyethylene, and results on optimized lattice parameters, cohesive energy and the band structure utilizing 6-31G** basis sets are presented. Our results are also shown to be in excellent agreement with those obtained with traditional Bloch-orbital-based approaches.Comment: 15 Pages, RevTex, inludes four figures, Chem. Phys. Letts., in press (1998

Synchronization of Excitatory Neurons with Strongly Heterogeneous Phase Responses

In many real-world oscillator systems, the phase response curves are highly heterogeneous. However, dynamics of heterogeneous oscillator networks has not been seriously addressed. We propose a theoretical framework to analyze such a system by dealing explicitly with the heterogeneous phase response curves. We develop a novel method to solve the self-consistent equations for order parameters by using formal complex-valued phase variables, and apply our theory to networks of in vitro cortical neurons. We find a novel state transition that is not observed in previous oscillator network models.Comment: 4 pages, 3 figure

Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators

We show that a wide class of uncoupled limit cycle oscillators can be in-phase synchronized by common weak additive noise. An expression of the Lyapunov exponent is analytically derived to study the stability of the noise-driven synchronizing state. The result shows that such a synchronization can be achieved in a broad class of oscillators with little constraint on their intrinsic property. On the other hand, the leaky integrate-and-fire neuron oscillators do not belong to this class, generating intermittent phase slips according to a power low distribution of their intervals.Comment: 10 pages, 3 figure