# Download Stability of Critical Equilibrium States (Nonlinear science: theory & applications) fb2

**E.E. Shnol,E. E. Shnol,L.G. Khazin**

- Author:E.E. Shnol,E. E. Shnol,L.G. Khazin
- ISBN:0471935239
- ISBN13:978-0471935230
- Genre:
- Publisher:John Wiley & Sons Ltd (March 23, 1992)
- Pages:220 pages
- Subcategory:Mathematics
- Language:
- FB2 format1758 kb
- ePUB format1959 kb
- DJVU format1932 kb
- Rating:4.7
- Votes:610
- Formats:azw mobi lrf doc

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Sufficient stability conditions for an equilibrium state of a complex impulsive system are obtained. 22. L. G. Khazin and E. E. Shnol, Stability of Critical Equilibrium States. Some problems in the theory of control of the motion of mechanical systems require the use of. impulsive control. Hence, the importance of examining the stability of equilibrium states of complex sys. Nauchnyi Tsentr Biologicheskikh Issledo. vanii AN SSSR, Pushchino, 1985; Manchester Univ.

Stability of critical. Khazin, E. Shnol. Catherine Waterhouse translator. NONLINEAR CHEMICAL WAVES Peter J. Ortoleva This volume concentrates on chemical wave mechanics arising in reaction-transport systems. Its starting point, the chemical wave, is a disturbance in a macroscopic variable, like concentration or voltage, which propagates over long distances without attenuation. Shnol, Stability of Critical Equilibrium States (Nauchnyi Tsentr Biologicheskikh Issledovanii AN SSSR, Pushchino, 1985; Manchester Univ. An example of examining the stability of an equilibrium state in the degenerate critical case is discussed. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Math Sc. I, 1-148, Springer-Verlag. Shnol (1991) Stability of Critical Equilibrium States. Manchester University Press.

Systems with critical equilibria are not structurally stable: When parameters are perturbed, phase portraits of such systems undergo qualitative change - a bifurcation - near the equilibria. The first critical case ((lambda 0)) corresponds to saddle-node bifurcation; the second case ((lambda pm i omega)) corresponds to Andronov-Hopf bifurcation; critical cases of co-dimensions 2 and 3 correspond to more complicated bifurcations, some of which are not well-understood. Math Sc.

G. Stability of Critical Equilibrium States. Khazin, È. È. Shnol', The problem of the gravitational stability of a dust cloud, Dokl. Nauk SSSR, 185:5 (1969), 1018–1021. Shnol', Theory of a degenerate Fermi gas in an external field, TMF, 4:2 (1970), 239–245 ; Theoret. 4:2 (1970), 807–811.

On the stability of a circular system subjected to nonlinear dissipative . Shnol, Stability of Critical Equilibrium States (Center of Biological Studies, Pushchino, 1985).

On the stability of a circular system subjected to nonlinear dissipative forces. S. A. Agafonov (Bauman Moscow State Technical University, 2-ya Baumanskaya 5, Moscow, 105005 Russia). Merkin, Introduction to Theory of Stability of Motion (Nauka, Moscow, 1971). Seyranian, "Stabilization and Destabilization of a Circulatory System by Small Velocity-Dependent Forces," J. Sound Vibr. 283 (3-5), 781-800 (2005).

The critical equilibrium states have been the subject of a large number of studies. Khazin, L. and Shnol, E. Stability of Critical Equilibrium States (Manchester University Press). Here, we shall consider only the two most common and simple cases, where the characteristic equation. 5, the above critical equilibrium state lies in an invariant C -smooth center manifold defined by an equation of the form y (a ), where (x) vanishes at the origin along with its first derivative. Our investigation of the stability of a critical equilibrium state will make use of Lyapunov functions.

To analyze the stability the bifurcation approach was used that based on linearization of the equilibrium equations in the neighborhood of the obtained solutions. The bifurcation point was defined as such value of the "loading" parameter (Burgers vector magnitude, stretch ratio or other strain characteristic) for which the linearized problem has a nontrivial solution.