On stability boundaries of conservative systems

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

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Stability boundaries of gas hydrates helped by methane—structure-H hydrates of methylcyclohexane and cis-1,2-dimethylcyclohexane

Chemical Engineering Science ◽

10.1016/s0009-2509(02)00518-3 ◽

2003 ◽

Vol 58 (2) ◽

pp. 269-273 ◽

Cited By ~ 144

Author(s):

Toshiyuki Nakamura ◽

Takashi Makino ◽

Takeshi Sugahara ◽

Kazunari Ohgaki

Keyword(s):

Gas Hydrates ◽

Stability Boundaries

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Quiescent Gap Solitons in Coupled Nonuniform Bragg Gratings with Cubic-Quintic Nonlinearity

Applied Sciences ◽

10.3390/app11114833 ◽

2021 ◽

Vol 11 (11) ◽

pp. 4833

Author(s):

Afroja Akter ◽

Md. Jahedul Islam ◽

Javid Atai

Keyword(s):

Numerical Stability ◽

Bragg Gratings ◽

Stability Boundaries ◽

Quintic Nonlinearity ◽

Numerical Stability Analysis ◽

Gap Solitons ◽

The Stability ◽

Dual Core

We study the stability characteristics of zero-velocity gap solitons in dual-core Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity. The model supports two disjointed families of gap solitons (Type 1 and Type 2). Additionally, asymmetric and symmetric solitons exist in both Type 1 and Type 2 families. A comprehensive numerical stability analysis is performed to analyze the stability of solitons. It is found that dispersive reflectivity improves the stability of both types of solitons. Nontrivial stability boundaries have been identified within the bandgap for each family of solitons. The effects and interplay of dispersive reflectivity and the coupling coefficient on the stability regions are also analyzed.

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The existence of periodic solutions for nonlinearly perturbed conservative systems

Nonlinear Analysis ◽

10.1016/0362-546x(79)90097-x ◽

1979 ◽

Vol 3 (5) ◽

pp. 697-705 ◽

Cited By ~ 11

Author(s):

James R. Ward

Keyword(s):

Periodic Solutions ◽

Conservative Systems ◽

Existence Of Periodic Solutions

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DRY TURBULENCE FROM A TIME-DELAYED CHUA'S CIRCUIT

Journal of Circuits System and Computers ◽

10.1142/s021812669300040x ◽

1993 ◽

Vol 03 (02) ◽

pp. 645-668 ◽

Cited By ~ 30

Author(s):

A. N. SHARKOVSKY ◽

YU. MAISTRENKO ◽

PH. DEREGEL ◽

L. O. CHUA

Keyword(s):

Difference Equation ◽

Stability Region ◽

Nonlinear Difference Equation ◽

Chua’S Circuit ◽

Stability Boundaries ◽

Chua's Circuit ◽

Infinite Dimensional ◽

Chaotic Region ◽

The Stability ◽

Left Portion

In this paper, we consider an infinite-dimensional extension of Chua's circuit (Fig. 1) obtained by replacing the left portion of the circuit composed of the capacitance C2 and the inductance L by a lossless transmission line as shown in Fig. 2. As we shall see, if the remaining capacitance C1 is equal to zero, the dynamics of this so-called time-delayed Chua's circuit can be reduced to that of a scalar nonlinear difference equation. After deriving the corresponding 1-D map, it will be possible to determine without any approximation the analytical equation of the stability boundaries of cycles of every period n. Since the stability region is nonempty for each n, this proves rigorously that the time-delayed Chua's circuit exhibits the "period-adding" phenomenon where every two consecutive cycles are separated by a chaotic region.

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Two-stream and filamentation instabilities for a light ion beam—plasma system

Journal of Plasma Physics ◽

10.1017/s0022377800012253 ◽

1987 ◽

Vol 37 (3) ◽

pp. 373-382 ◽

Cited By ~ 14

Author(s):

Toshio Okada ◽

Winfried Schmidt

Keyword(s):

Proton Beam ◽

Size Effects ◽

Ion Beam ◽

Plasma Heating ◽

Finite Size ◽

Stability Conditions ◽

Plasma System ◽

Finite Size Effects ◽

Stability Boundaries ◽

Gas Discharges

Electrostatic two-stream and electromagnetic filamentation instabilities for a light ion beam penetrating a plasma are investigated. The dispersion relations of these instabilities including the effect of plasma heating by the ion beam are solved analytically and numerically. Stability conditions are derived for propagation through a plasma. Attention is paid to the finite size effects of beams with small diameters of the order 0·1 cm typical for pinched gas discharges. The results are illustrated by plotting stability boundaries for a 100 keV proton beam propagating through a plasma.

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