We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively study the loop effect on network dynamics. A large...

By employing a nonlinear three-mode model, we study the band structure of Bose–Einstein condensates in Fourier-Synthesized optical lattices, where the nonlinearity comes from the mean field treatment of interaction between atoms. In linear case, we present the band structure of the system. It...

Using probabilistic approach, the transient dynamics of sparsely connected Hopfield neural networks is studied for arbitrary degree distributions. A recursive scheme is developed to determine the time evolution of overlap parameters. As illustrative examples, the explicit calculations of...

We report a new statistical general property in traveling salesman problem, that the nth-nearest-neighbor distribution of optimal tours verifies with very high accuracy an exponential decay as a function of the order of neighbor n. Defining the energy function as deviation λ from this...

Most papers about the evolutionary game on graph assume the statistic network structure. However, in the real world, social interaction could change the relationship among people. And the change of social structure will also affect people’s strategies. We build a coevolution model of...

We study theoretically a bistable system with time-delayed feedback driven by a weak periodic force. The effective potential function and the steady-state probability density are derived. The delay time and the strength of its feedback can change the shapes of the potential wells. In the...