Sentence examples for manifold of system from inspiring English sources

The plane (S+I+R= frac{Lambda}{mu}) is an invariant manifold of system (1.3), which is globally attractive in (mathbb{R}^{3}_).

Note that the (x_{i} -axis ((i=1,2,3)), the invariable manifold of system (4.6), and the orbits of system (4.6) do not intersect each other.

And μ m is called the mth singular point quantity at the origin on center manifold of system (17) or (8) or (2).

For the succession function in (13), if v2(2π) = v3(2π) = · · · = v2k(2π) = 0 and v2k+1(2π) ≠ 0, then the origin is called the fine focus or weak focus of order k, and the quantity of v2k+1(2π) is called the k th focal value at the origin on center manifold of system (8) or (2), k = 1, 2,.... Remark 1.

For the mth singular point quantity and the mth focal value at the origin on center manifold of system (8), i.e. µ m and v2m+1, m = 1, 2,..., we have the following relation: v 2 m + 1 ( 2 π ) = i π μ m + i π ∑ k = 1 m - 1 ξ m ( k ) μ k (20).

When (b=0), the center manifold of system (1.2) is (w=0), and the restriction of system (1.2) in the center manifold becomes dot{x}=y,qquad dot{y}=mx-ny-px^{3}. (2.8) If (n=0), then system (2.8) is a Hamilton system with the Hamiltonian function (H x,y)=frac{1}{2}y^{2}-frac{m}{2}x^{2}+ frac{p}{4}x^{4}x.

Attracting and saddle slow manifolds of system (32) can be extended by the flow in forward and backward time, respectively, to study the SAOs that occur in the vicinity of the lower fold curve (F_{1}).

determines the integral manifold of the system of differential equations (25).

A general repetitive learning control structure based on the invariant manifold of chaotic system is given.

Conditions are stated for the introduction of a Hopf bifurcation at a given location on the equilibrium manifold of a system of ODEs.

We show that the stable manifold of this system separates the positive quadrant of initial conditions into basins of attraction of two types of asymptotic behavior.