Abstract. The properties of the mean first passage time in a system characterized by multiple periodic attractors are studied. Using a transformation from a high dimensional space to 1D, the problem is reduced to a stochastic process along the path from the fixed point attractor to a saddle point located between two neighboring attractors. It is found that the time to switch between attractors ...

We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in primal variable, we first restart scheme for this problem. gradient noises obey sub-Gaussian distributions, oracle complexity our strictly better than any existing methods, even deterministic case. Furthermore, each problem parameter i...

In this work we show the existence existence and uniqueness of traveling waves for diffusive-dispersive conservation laws with flux function in C1(R), by using phase plane analysis. Also we estimate the domain of attraction of the equilibrium point attractor corresponding to the right-hand state. The equilibrium point corresponding to the left-hand state is a saddle point. According to the phas...

We propose a conjecture for the limit of mean-field spin glasses with bipartite structure, and show that conjectured is an upper bound. The described in terms solution infinite-dimensional Hamilton-Jacobi equation. A fundamental difficulty problem nonlinearity this equation not convex. also question possibility to characterize saddle-point problem.

This paper aims to study a degenerate parabolic problem for solenoidal vector field in which the time derivative acts on moving body. We propose fully-discrete finite element scheme combined with backward Euler’s method saddle-point variational formulation. The convergence of this numerical is proved and error estimates some stable pairs are also established.

An adaptive feedback method for tracking and stabilizing unknown or slowly varying saddle type steady states of conservative dynamical systems is described. We demonstrate that a conservative saddle point can be stabilized with neither unstable nor stable filter technique. Meanwhile, a controller, involving both filters in parallel, works perfectly. As a specific example, the Lagrange point L2 ...