An ω-symmetrically coupled system consisting of identical fractional-order differential systems including chaotic and nonchaotic systems is investigated in this paper. Such a coupled system has, in its synchronous state, a mode decomposition by which the linearized equation can be decomposed into motions transverse to and parallel to the synchronous manifold. Furthermore, the decomposition can induce a sufficient condition on synchronization of the overall system, which guarantees, if satisfied, that a group synchronization is achieved. Two typical numerical examples, fractional Brusselators and the fractional Rossler system, are used to verify the theoretical prediction. The theoretical analysis and numerical results show that the lower the order of the fractional system, the longer the time for achieving synchronization at a fixed coupling strength.

We model a synthetic gene regulatory network in a microbial cell, and investigate the effect of noises on cell-cell communication in a well-mixed multicellular system. A biologically plausible model is developed for cellular communication in an indirectly coupled multicellular system.Without extracellular noises, all cells, in spite of interaction among them, behave irregularly due to independent intracellular noises. On the other hand, extracellular noises that are common to all cells can induce collective dynamics and stochastically synchronize the multicellular system by actively enhancing the integrated interchange of signaling molecules.

We investigate a general coupled noisy system with time delays, which may be applied to biologically plausible systems for cell-cell communication in a simplified context. The main conclusion is that appropriate noise intensities and coupling strengths are capable of driving the system to be synchronous. We first provide an analytical treatment for the synchronization process, based on the essential phase-locking mechanism, and then derive sufficient conditions which, if satisfied, ensure existence of the synchrony solution. Finally, a multi-cell system with a synthetic gene regulatory network, which contains both intracellular and extracellular noises and time delays, is adopted to demonstrate effects of extracellular noises and couplings on synchronization.

The responses of nonlinear dynamics of two classes to coupling are investigated. It is shown both analytically and numerically that coupling has an excitation ability in a network of the linearly coupled systems. That is, when an uncoupled system is degenerated to a stable steady state from a limit cycle but in the "marginal" state due to the system parameter, an appropriate coupling strength can excite the limit cycle such that the coupled systems exhibit synchronous oscillation; when the uncoupled system is in a stable limit cycle but close to a chaotic attractor, a certain coupling strength can induce the chaotic attractor such that the coupled systems reach chaotic synchronization. Such excitation functions of coupling are different from its traditional role where coupling mainly synchronizes the coupled systems with the original dynamics of the uncoupled system.

Motivation: Protein structure alignment is one of the most important computational problems in molecular biology and plays a key role in protein structure prediction, fold family classification, motif finding, phylogenetic tree reconstruction and so on. From the viewpoint of computational complexity, a pairwise structure alignment is also a NP-hard problem, in contrast to the polynomial time algorithm for a pairwise sequence alignment. Results: We propose a method for solving the structure alignment problem in an accurate manner at the amino acid level, based on a mean field annealing technique. We define the structure alignment as a mixed integer-programming (MIP) problem. By avoiding complicated combinatorial computation and exploiting the special structure of the continuous partial problem, we transform the MIP into a reduced non-linear continuous optimization problem (NCOP) with a much simpler form. To optimize the reduced NCOP, a mean field annealing procedure is adopted with a modified Potts model, whose solution is generally identical to that of the MIP. There is no 'soft constraint' in our mean field model and all constraints are automatically satisfied throughout the annealing process, thereby not only making the optimization more efficient but also eliminating many unnecessary parameters that depend on problems and usually require careful tuning. A number of benchmark examples are tested by the proposed method with comparisons to several existing approaches.