STABILITY OF STEADY-STATE SOLUTIONS IN MULTIDIMENSIONAL COUPLED MAP LATTICES

2004 ◽  
Vol 14 (08) ◽  
pp. 2689-2699
Author(s):  
MIROSLAVA DUBCOVÁ ◽  
DANIEL TURZÍK ◽  
ALOIS KLÍČ
Keyword(s):  
Steady State ◽  
Coupled Map Lattices ◽  
Multidimensional Lattice ◽  
Spatially Periodic ◽  
Spatially Homogeneous ◽  
Periodic Steady State ◽  
The Stability ◽  
Linearized Operator ◽  
Steady State Solutions

Coupled map lattices with multidimensional lattice are considered. A method for the determination of the stability of spatially homogeneous and spatially periodic steady-state solutions is derived. This method is based on the determination of the spectrum of the linearized operator by means of Gelfand transformation of some appropriate Banach algebra. The results are applied to several examples.

STABILITY OF SPATIALLY PERIODIC SOLUTIONS IN COUPLED MAP LATTICES

2003 ◽  
Vol 13 (02) ◽  
pp. 343-356 ◽  
Author(s):  
M. DUBCOVÁ ◽  
A. KLÍČ ◽  
P. POKORNÝ ◽  
D. TURZÍK
Keyword(s):  
Steady State ◽  
Periodic Solutions ◽  
Nonlinear Evolution ◽  
Linear Operators ◽  
Coupled Map Lattices ◽  
Evolution Operators ◽  
Spatially Periodic ◽  
The Stability ◽  
Steady State Solutions ◽  
Theoretical Results

Stability of steady-state solutions of 1-dim coupled map lattices is studied. The stability is determined by the spectrum of linear operators on two-sided sequences of vectors in [Formula: see text] arising as a linearization of the corresponding nonlinear evolution operators. Theoretical results are applied to several examples.

ON PERSISTENCE AND STABILITY OF COUPLED MAP LATTICES

2001 ◽  
Vol 04 (02n03) ◽  
pp. 191-205
Author(s):  
E. AHMED ◽  
A. S. HEGAZI
Keyword(s):  
Steady State ◽  
Coupled Map Lattices ◽  
Circle Map ◽  
Josephson Junction Arrays ◽  
Winfree Model ◽  
Cml Model ◽  
The Stability ◽  
Junction Arrays ◽  
Steady State Solutions ◽  
Stability Results

Linear stability of homogeneous and inhomogeneous steady state solutions for coupled map lattices (CML) are studied. Some persistence problems in CML are discussed and applied to immune and an economic models. The stability results are applied to CML motivated by forced circle map, Winfree model, Josephson junction arrays and an ecological CML model. Global stability results for some CML systems are given.

STABILITY OF STEADY STATE AND TRAVELING WAVES SOLUTIONS IN COUPLED MAP LATTICES

2008 ◽  
Vol 18 (01) ◽  
pp. 219-225 ◽  
Author(s):  
DANIEL TURZÍK ◽  
MIROSLAVA DUBCOVÁ
Keyword(s):  
Steady State ◽  
Essential Spectrum ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Linear Operators ◽  
Coupled Map Lattices ◽  
Basic Tool ◽  
Wave Solutions ◽  
The Stability

We determine the essential spectrum of certain types of linear operators which arise in the study of the stability of steady state or traveling wave solutions in coupled map lattices. The basic tool is the Gelfand transformation which enables us to determine the essential spectrum completely.

Stability Considerations in Thermoelastic Contact

1980 ◽  
Vol 47 (4) ◽  
pp. 871-874 ◽  
Author(s):  
J. R. Barber ◽  
J. Dundurs ◽  
M. Comninou
Keyword(s):  
Steady State ◽  
Perturbation Method ◽  
Energy Function ◽  
First Principles ◽  
Dimensional Model ◽  
Contact Conditions ◽  
One Dimensional ◽  
Thermoelastic Contact ◽  
The Stability ◽  
Steady State Solutions

A simple one-dimensional model is described in which thermoelastic contact conditions give rise to nonuniqueness of solution. The stability of the various steady-state solutions discovered is investigated using a perturbation method. The results can be expressed in terms of the minimization of a certain energy function, but the authors have so far been unable to justify the use of such a function from first principles in view of the nonconservative nature of the system.

Bifurcation Analysis of a Diffusive Activator–Inhibitor Model in Vascular Mesenchymal Cells

2015 ◽  
Vol 25 (10) ◽  
pp. 1530026 ◽  
Author(s):  
Rui Yang ◽  
Yongli Song
Keyword(s):  
Steady State ◽  
Center Manifold ◽  
Normal Forms ◽  
Mesenchymal Cells ◽  
Positive Equilibrium ◽  
Normal Form Theory ◽  
Form Theory ◽  
Spatially Homogeneous ◽  
The Stability ◽  
Activator Inhibitor

In this paper, a diffusive activator–inhibitor model in vascular mesenchymal cells is considered. On one hand, we investigate the stability of the equilibria of the system without diffusion. On the other hand, for the unique positive equilibrium of the system with diffusion the conditions ensuring stability, existence of Hopf and steady state bifurcations are given. By applying the center manifold and normal form theory, the normal forms corresponding to Hopf bifurcation and steady state bifurcation are derived explicitly. Numerical simulations are employed to illustrate where the spatially homogeneous and nonhomogeneous periodic solutions and the steady states can emerge. The numerical results verify the obtained theoretical conclusions.

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