Sentence examples for existence of period from inspiring English sources

Since such a minimality can be used to prove the minimal periods of solutions, it has been used to study the existence of period solutions with prescribed minimal period to ordinary differential equations (cf. [22 25]).

That is, we will investigate the global behavior of (1.1), including the global asymptotical stability of zero equilibrium, the existence of unbounded solutions, the existence of period two solutions, the existence of oscillatory solutions, the existence and asymptotic behavior of nonoscillatory solutions of the equation.

We mainly study the global behavior of the nonlinear difference equation in the title, that is, the global asymptotical stability of zero equilibrium, the existence of unbounded solutions, the existence of period two solutions, the existence of oscillatory solutions, the existence, and asymptotic behavior of non-oscillatory solutions of the equation.

We establish the relations for the local stability of equilibriums and the existence of period-two solutions.

Firstly, we study the stability of the equilibria of the system and the existence of period-two bifurcation by analyzing the characteristic equation.

What the thought experiment does seem to show, however, is that it is possible for rational beings to have at least some evidence for the existence of periods of empty time in their world.

Theorem 3.3 A necessary and sufficient condition for the existence of periodic solutions of period p of Equation (11) is that ∑ k = 0 p - 1 y T ( k + 1 ) f ( k ) = 0, (42).

The results of numerical simulations for the two-degree-of-freedom nonlinear equation exhibit the existence of the period, multi-period and chaotic responses with the variation of the excitations, which demonstrate that those motions appear alternately.

However, except the questions of the existence of periodic solutions with prescribed periods, little information was given on the periods of periodic solutions.

One of the natural problems in dynamical systems is the study of the existence of periodic points of least period exactly n.

The shift homeomorphism (sigma_{f}) preserves topological entropy of f, as well as many other dynamical properties such as existence of periodic orbits of given period, shadowing property, and topological mixing [12].