Sentence examples for system at the origin from inspiring English sources

In Section 2, we analyze the Hopf bifurcation of the extended Lorenz system at the origin.

Then, the EID-based approach is used to globally and asymptotically stabilize the system at the origin.

After that, we construct an equivalent-input-disturbance- (EID-) based control system to globally stabilize the transformed system at the origin.

Since the power is not restricted to be larger than or equal to one, the linearization of the system at the origin may fail.

One of the difficulties of the problem is that the Jacobian linearization of our system at the origin may not be stabilizable.

The main objective is to analyze the performance of this system at different operating conditions, including those giving rise to chaos, and to design a controller with an overparameterized structure to stabilize the system at the origin.

The singularity of cylindrical or spherical coordinate systems at the origin imposes certain regularity conditions on the spectral expansion of any infinitely differentiable function.

An isolated critical point (O 0, 0)) is called a nilpotent singular point if the linear part of systems has double zero eigenvalues but the matrixes of the linearized systems at the origin are not identically null.

When the origin of system (1.1) is a 11th-order weak focus, the first Lyapunov constant of system (5.3) at the origin is V_{1}=2 (2 a_{22} + 3 b_{13}) varepsilon^{3} (2 + b40varepsilonlambda )^{2}neq0, when (varepsilonrightarrow0). Similarly, summarizing the above results yields the following theorem.

From Lemma 2.1 we know that when (H1) and (H2) hold, then system (1.4) at the origin will undergo a BT bifurcation.

Chronologically, the latter system is at the origin of this type of measurement, when it was realized that the exchange current deduced from Tafel plots was identical to that existing between the solution and the deposited catalyst.