Sentence examples for the positive orbit from inspiring English sources

The set (C^ z)={Pi x,t)|tin {mathbb {R}}}) is called the positive orbit of Z.

The set C^ z)=bigl{ Pi z,t)| tin R_bigr} is called the positive orbit of z.

Our approach is to find a suitable set of initial positions satisfying the requirement that the positive orbits of (1.5) starting from this set approach the x-axis, y-axis and z-axis as n tends to infinity.

In this part, we arbitrarily select a point Q ≠ O and Q is not in any of the stable manifolds, then the positive half orbit through the point Q will run out of this part or Ω Q is a closed orbit or a singular closed trajectory, where Ω Q is a positive limit set of  L Q.

It follows from (3.4) that, for any given compact set E in the interior of (R^{3}_), there is a positive orbit of (2.2) leaving ultimately E, which will not return to E afterwards.

Denote by (omega phi)) the omega limit set of the positive half-orbit (gamma^{phi}={Phi(t phi: tge0}) and (X_{partial}={phiinpartial X_{0}: Phi(t phiinpartial X_{0},tge0}).

Ω 1 is also a global compact attractor of system (1) since it attracts all positive orbits with an initial value ( S 0, I 0, R 0 ) ∈ R + 3. The basic reproductive number, R 0, is fundamental and widely used in the study of epidemiological models.

Furthermore, there exists the global stable manifold that separates the positive quadrant so that all orbits below this manifold are asymptotic to and all orbits above this manifold are asymptotic to All orbits that start on are attracted to The global unstable manifold is the graph of a continuous, unbounded, strictly decreasing function.

Furthermore, there exists the global stable manifold that separates the positive quadrant so that all orbits below this manifold are asymptotic to and all orbits above this manifold are asymptotic to All orbits that start on are attracted to The global stable manifold is the graph of a continuous, unbounded, strictly increasing function.

Furthermore, there exists the global stable manifold that separates the positive quadrant so that all orbits below this manifold are asymptotic to and all orbits above this manifold are attracted to equilibrium All orbits that start on are attracted to The global unstable manifold is the graph of a continuous, unbounded, strictly decreasing function with end point.

Conversely, if the energy is positive (unbound orbits, also called "scattered orbits"), the eccentricity is greater than one and the orbit is a hyperbola.