Globally attracting

In spite of almost global attraction of the critical load concept, the quantitative assessment of critical load values is connected till now with some uncertainties. The phrase significant harmful effects in the definition of critical load is of course susceptible to interpretation, depending on the kind of effects considered and the amount of harm accepted (De Vries and Bakker, 1998a, 1998b). Regarding the effects considered in terrestrial ecosystems, a distinction can be made in effects on ... 

A positive value of X arises because the trajectories in state space for chaotic behavior are diverging in the mean. Conversely, adjacent trajectories in a system which possesses a globally attracting limit cycle will converge. Values of X for periodic systems can be obtained by perturbing the reactor from a periodic state and observing the rate of convergence back to the periodic orbit. In Fig. 4 is shown the result of such an... 

We say that x = 0 is an attracting fixed point in Figures 5.1.5a-c all trajectories that start near x approach it as z —> oo. That is, x(z) —> x as z oo. in fact x attracts all trajectories in the phase plane, so it could be called globally attracting. 

Solution Numerical simulations indicate that the system has a globally attracting limit cycle for all r > 313 (Sparrow 1982). In Figures 9.5.4 and 9.5.5 we plot a typical solution for r = 350 note the approach to the limit cycle. 

Capasso, V, Di Liddo, A. Global attractivity for reaction-diffusion systems. The case of nondiagonal diffusion matrices. J. Math. Anal. Appl. 177(2), 510-529 (1993). http //dx. doi.org/10.1006/jmaa.1993.1274... 

If we now consider the forces exerted between two particles (or more generally, between several particles), we can assume to a first approximation that the van der Waals forces are additive. Within a given particle, each atom or molecule is thus subject to attractive forces from all the atoms of the neighbouring particles. The global attraction can be calculated for each geometrical arrangement of the particles. 

Consider a liquid droplet in equilibrium with its vapour (see Fig. 3.6). Each molecule is subject to attractive van der Waals forces due to each of its neighbours. Inside, the medium is isotropic (i.e., it has identical properties in all directions) and it can be assumed that the mean global attraction exerted on a molecule inside the droplet by its neighbours is zero. The same is not true for a molecule located near the outer surface of the droplet, which is attracted... 

In the case of large 6 a weakness of attractors appears as a rule in the form of nonstationary waves with parameters that are varied in narrow intervals closed to values of the dominating waves. At any case we ll use a name the dominating wave in accordance with definition introduced above but its global attractive capacity must be studied in numerical experiments in frame of (9). If the limiting wave is formed then it will be referred as the tested dominating wave. 

Dynamical questions that can be answered concern stability and whether a steady state or region of concentration space is globally attracting. There is quite a powerful technique used for finding globally attracting steady states, even for networks where other steady states are unstable. 

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