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Hence, next we will consider the center problem of the origin and ( 1, 0 ).
Without loss of generality, we only need to consider the center problem of ( 1, 0 ).
At first, we investigate the center problem of four symmetrical singular points.
They also proved for this system the existence of a Lyapunov function, and they solved theoretically the center problem for such a system.
Remember that the so-called stability problem and the center problem can be solved for smooth non-degenerate critical points via the Lyapunov constants.
However, more and more attention has been paid to the center problem and bifurcation of limit cycles of a system with a nilpotent critical point recently.
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In the hub center problem, the main objective is one of minimizing the maximum distance/cost between origin destination pairs.
Hyytiä and Virtamo [25] studied how to avoid the crowded center problem by analyzing the load probability in a dense network.
After considering the weak center problem, ulteriorly we investigate the bifurcation of critical periods from a weak center.
For third-order nilpotent critical points of a planar dynamical system, the analytic center problem was completely solved by using the integrating factor method [18].
Big information technology suppliers like I.B.M., Hewlett-Packard and Sun Microsystems have stepped forward with products and services to address the data center problem.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com