Search results
Results from the WOW.Com Content Network
If all eigenvalues of J are real or complex numbers with absolute value strictly less than 1 then a is a stable fixed point; if at least one of them has absolute value strictly greater than 1 then a is unstable. Just as for n =1, the case of the largest absolute value being 1 needs to be investigated further — the Jacobian matrix test is ...
[1] Diversification and integration in the financial network determine whether and how failures will spread. Using the data on cross-holdings of organizations and on the value of organizations, it is possible to construct the dependency matrix to simulate cascades in the financial network.
The Nyquist plot for () = + + with s = jω.. In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer Felix Strecker [] at Siemens in 1930 [1] [2] [3] and the Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, [4] is a graphical technique ...
Routh–Hurwitz stability criterion; Vakhitov–Kolokolov stability criterion; Barkhausen stability criterion; Stability may also be determined by means of root locus analysis. Although the concept of stability is general, there are several narrower definitions through which it may be assessed: BIBO stability; Linear stability; Lyapunov stability
Many algorithms solve this problem by starting with an initial approximation x 0 to , for instance x 0 = 1.4, and then computing improved guesses x 1, x 2, etc. One such method is the famous Babylonian method, which is given by x k+1 = (x k + 2/x k)/2. Another method, called "method X", is given by x k+1 = (x k 2 − 2) 2 + x k.
For a rational and continuous-time system, the condition for stability is that the region of convergence (ROC) of the Laplace transform includes the imaginary axis.When the system is causal, the ROC is the open region to the right of a vertical line whose abscissa is the real part of the "largest pole", or the pole that has the greatest real part of any pole in the system.
In certain cases, von Neumann stability is necessary and sufficient for stability in the sense of Lax–Richtmyer (as used in the Lax equivalence theorem): The PDE and the finite difference scheme models are linear; the PDE is constant-coefficient with periodic boundary conditions and has only two independent variables; and the scheme uses no ...
In this context, the cascading failure is known by the term cascade failure. A cascade failure can affect large groups of people and systems. The cause of a cascade failure is usually the overloading of a single, crucial router or node, which causes the node to go down, even briefly. It can also be caused by taking a node down for maintenance ...