Here we modify this idea and gluing two (C^{1}) paths of solutions together to obtain a continuous path of solutions, by which we can obtain the rotating periodic solutions (specially, quasi-periodic periodic solutions) of (1.1).
Here we modify this idea and gluing two (C^{1}) paths of solutions together to obtain a continuous path of solutions, by which we can track along the trajectory to obtain the rotating periodic solutions (specially, quasi-periodic solutions) of (1.1).
The problems (13) and (14) are equivalent in the sense that the path of solutions of (13) parametrized by a positive β matches with the solution path (14) as τ varies.
Following the (C^{1}) path of solutions of the Cauchy problem starting from a simpler auxiliary equation corresponding to (lambda=0), one can obtain the desired periodic solutions corresponding to (lambda=1).
The velocity is initialized to be zero in the first iteration., and are parameters of the PSO used to adjust the influence to the path of solutions from a particle's best location and the group's best location.
We can write the optimality condition as follows: (3) Our goal is to compute the path of solutions of (3) for all the λ.
PATH formulates the pairwise network alignment as a graph matching problem and solves its convex and concave relaxations by iteratively updating the weights and following the path of solutions thus created.
The method starts by solving the convex relaxation, and then iteratively solves a linear combination of the convex and concave relaxations by gradually increasing the weight of the concave relaxation and following the path of solutions thus created.
In that case, we propose to use a recent state-of-the-art approximate methods for graph matching (Zaslavskiy et al., 2008b), which tracks a path of solutions for a family of relaxed problems, as well as a new, faster and more direct gradient-based method, which bears similarities with the IsoRank method.
end{cases} (1.2) The main aims of this contribution are to investigate the extinction, stochastic permanence, the limit of the average in time of the sample paths of solutions and global attractivity, which is a continuation of previous work [1, 3, 4].
