Often to detect the behavior in a small neighborhood of the equilibrium, instead of the Hamiltonian H one considers the normal form
truncated to some order
Now, by setting [K.sub.kl], k + l = 2, ..., 2[n.sub.r] + 1 equal to zero we define the coefficients [h.sup.kl] of transformation (B.1), while the rest of the resonant terms of the odd order, [c.sub.i] = [K.sub.i+1,i], i = 1, ..., [n.sub.r], constitute the desirable normal form
be the Smith normal form
of matrix A, where U [member of] GL(m, R) and V [member of] GL(n, R).
The classification of the student answer (normal form
) in the form of waterfall model.
Proposition 1 There exists an algorithm that, given a sword [sigma] of height h, returns a normal form
In Section 3, by using an extended method of multiple scales, we obtained the normal form
of the Hopf bifurcation.
The normal form
method and the center manifold theory are used to analyze the double Hopf bifurcation for system.
Previous studies showed that the normal form
of the protein is an enzyme that maintains the structure and integrity of a person's DNA.
Jandad Spinghar, the Election Watch Afghanistan's (EWA) chief, said the electoral process was not in its normal form
that's why initial results had to be delayed.
A normal form
could be printed for ` 200, the committee held.
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are homogeneous polynomials of degree j in [??] and [epsilon], after dropping the hats for simplification of notations, system (42) can be put into the normal form
In this subsection, we will determine the direction and stability of Hopf bifurcations by calculating explicitly the normal form
of system (2) on the associated two-dimensional (2D) center manifold.