A lot of works has been devoted to stability analysis of a stationary point for linear and non-linear systems of stochastic di erential equations. Here we consider the stability of an invariant compact manifold of a non-linear system. To this end we derive a linearized system for orthogonal displacements of a solution from the manifold. We introduce notions of Lyapunov exponents, moment Lyapuno...

different discrete models of population dynamics of certain insects have been investigated under various feasible conditions within the framework of nonlinear dynamics. evolutionary phenomena are discussed through bifurcation analysis leading to chaos. some tools of nonlinear dynamics, such as lyapunov characteristic exponents (lce), lyapunov numbers, correlation dimension, etc. are calculated ...

Constraints are found on the spatial variation of finite-time Lyapunov exponents of two- and three-dimensional systems of ordinary differential equations. In a chaotic system, finite-time Lyapunov exponents describe the average rate of separation, along characteristic directions, of neighboring trajectories. The solution of the equations is a coordinate transformation that takes initial conditi...

We formulate the Wolff algorithm as a site-bond percolation problem, apply it to the ferromagnetic and antiferromagnetic planar triangular spin models, and study the percolation critical behavior using Anite-size scaling. In the former case the Wold' algorithm is successful as an accelerating algorithm, whereas in the latter case it is not. We found the percolation temperatures and the cluster ...

Classically, percolation critical exponents are linked to the power laws that characterize percolation cluster fractal properties. It is found here that the gradient percolation power laws are conserved even for extreme gradient values for which the frontier of the infinite cluster is no more fractal. In particular the exponent 7/4 which was recently demonstrated to be the exact value for the d...

‎we study the existence of soliton solutions for a class of‎ ‎quasilinear elliptic equation in $mathbb{textbf{r}}^2$ with critical exponential growth‎. ‎this model has been proposed in the self-channeling of a‎ ‎high-power ultra short laser in matter‎.