Abstract The pervasiveness of multi-stability in nonlinear dynamical systems calls for novel concepts stability and a consistent quantification long-term behavior. basin is global metric that builds on estimating the attraction volumes by Monte Carlo sampling. computation involves extensive numerical time integrations, attractor characterization, clustering trajectories. We introduce , an open-...

We study the long time behavior of the solution X(t, s, x) of a 2D-Navier-Stokes equation subjected to a periodic time dependent forcing term. We prove in particular that as t → ∞, E[φ(X(t, s, x))] approaches a periodic orbit independently of s and x for any continuous and bounded real function φ. 2000 Mathematics Subject Classification AMS: 76D05, 60H15,37A25

We give conditions for the existence, uniqueness, and asymptotic stability of periodic solutions of a second-order differential equation with piecewise linear restoring and 2fl-periodic forcing where the range of the derivative of the restoring term possibly contains the square of an integer. With suitable restrictions on the restoring and forcing in the undamped case, we give a necessary and s...

By applying critical point theory, the multiplicity of periodic solutions to second-order discrete Hamiltonian systems with partially periodic potentials was considered. It is noticed that, in this paper, the nonlinear term is growing linearly and main results extend some present results. c ©2017 all rights reserved.

A patient with spontaneous periodic hypothermia who had both a lipoma and agenesis of the corpus callosum is described. Spontaneous periodic hypothermia associated with corpus callosum abnormalities is a distinct entity and although the mechanism underlying the hypothermic episodes is unexplained, the term "diencephalic autonomic epilepsy" does not seem appropriate.

We consider first order periodic differential inclusions in R . The presence of a subdifferential term incorporates in our framework differential variational inequalities in R . We establish the existence of extremal periodic solutions and we also obtain existence results for the “convex” and “nonconvex”problems.

The second-order theory of partial coherence for scalar and TE or TM fields is developed for weakly periodic media, and the van Cittert-Zernike theorem of classical coherence theory is generalized for such media. The coherence properties of a wave field, generated by a quasi-homogeneous source distribution at the entrance plane of a finite weakly periodic medium, are calculated both inside such...

In this paper, the existence of 2 positive periodic solutions for n species non-autonomous Lotka-Volterra cooperative systems with harvesting terms is established by using Mawhin’s continuation theorem of coincidence degree theory and matrix inequality. An example is given to illustrate the effectiveness of our results. Keywords—Multiple positive periodic solutions; Nonautonomous Lotka-Volterra...

In this paper, we propose a technique for determining a source term in an inverse heat conduction problem (IHCP) using Radial Basis Functions (RBFs). Because of being very suitable instruments, the RBFs have been applied for solving Partial Dierential Equations (PDEs) by some researchers. In the current study, a stable meshless method will be pro- posed for solving an (I...

We describe a simple heterodyne laser interferometer that has subnanometer periodic errors and is applicable to industrial fields. Two spatially separated beams can reduce the periodic errors, and the use of a right-angle prism makes the optical configuration much simpler than previous interferometers. Moreover, the optical resolution can be enhanced by a factor of 2, because the phase change d...