scholarly journals Stability analysis of linear Volterra equations on time scales under bounded perturbations

2016 ◽  
Vol 59 ◽  
pp. 6-11 ◽  
Author(s):  
Eleonora Messina ◽  
Antonia Vecchio
Keyword(s):  
Stability Analysis ◽  
Time Scales ◽  
Volterra Equations ◽  
Bounded Perturbations

scholarly journals Stability analysis in terms of two measures for dynamic systems on time scales

1993 ◽  
Vol 6 (4) ◽  
pp. 325-344 ◽  
Author(s):  
Billûr Kaymakçalan
Keyword(s):  
Stability Analysis ◽  
Time Scales ◽  
Dynamic Systems ◽  
Lyapunov’S Second Method ◽  
Two Measures ◽  
Set Up ◽  
Stability Results ◽  
Stability Concepts ◽  
Single Set

Using the theory of Lyapunov's second method developed earlier for time scales, we extend our stability results to two measures which give rise to unification of several stability concepts in a single set up.

scholarly journals Exponential Stability of Periodic Solution to Wilson-Cowan Networks with Time-Varying Delays on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Jinxiang Cai ◽  
Zhenkun Huang ◽  
Honghua Bin
Keyword(s):  
Periodic Solution ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Time Scales ◽  
Continuous Time ◽  
Lyapunov Functional ◽  
Contraction Mapping ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Time Varying

We present stability analysis of delayed Wilson-Cowan networks on time scales. By applying the theory of calculus on time scales, the contraction mapping principle, and Lyapunov functional, new sufficient conditions are obtained to ensure the existence and exponential stability of periodic solution to the considered system. The obtained results are general and can be applied to discrete-time or continuous-time Wilson-Cowan networks.

scholarly journals Linearized stability analysis of discrete Volterra equations

2004 ◽  
Vol 294 (1) ◽  
pp. 310-333 ◽  
Author(s):  
Yihong Song ◽  
Christopher T.H. Baker
Keyword(s):  
Stability Analysis ◽  
Volterra Equations ◽  
Linearized Stability

Reaction-Diffusion Dissipative Systems—Detailed Stability Analysis-Pattern of Growth and Effect of Inhomogenity

1984 ◽  
Vol 39 (9) ◽  
pp. 899-916
Author(s):  
P. J. Nandapurkar ◽  
V. Hlavacek ◽  
J. Degreve ◽  
R. Janssen ◽  
P. Van Rompay
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Time Scales ◽  
Bifurcation Point ◽  
Selection Process ◽  
Reaction Diffusion ◽  
Dissipative Systems ◽  
Local Concentration ◽  
Fast Variable ◽  
Steady State Mode

A detailed stability analysis of the one dimensional steady state solutions for the Brusselator model under the conditions of diffusion of initial (non-autocatalytic) components has been performed both for zero flux as well as fixed boundary conditions. In addition to subcritical as well as supercritical bifurcations, situations have been observed where all solution branches at a bifurcation point are unstable. A case of degenerate steady state bifurcation (2 solutions emanating from the same bifurcation point) has also been noticed. A transient simulation of the system in growth reveals the importance of growth rate on the pattern selection process and suggests that the selection of branches at a bifurcation point may be influenced by perturbations/ fluctuations. It also indicates that a stability analysis of the bifurcation diagram alone cannot decide the state of the system in a transient process, and under certain situations complex behavior may be observed at limit points. Numerical calculations on coupled cells indicate that a heterogenity in the system can introduce multiple (two) time scales in the system. As the ratio of time scales increases, aperiodic or irregular oscillations are observed for the 'fast' variable. A combination of cells with one cell in a steady-state mode and the other in a periodic motion results in a combined motion of the entire system. For a distributed parameter system, a heterogenity can cause development of sharp local concentration gradients, alter the stability properties of steady state as well as periodic solutions and can cause partitioning of the system.

Voltage stability analysis in transient and mid-term time scales

1996 ◽  
Vol 11 (1) ◽  
pp. 146-154 ◽  
Author(s):  
T. Van Cutsem ◽  
C.D. Vournas
Keyword(s):  
Stability Analysis ◽  
Time Scales ◽  
Voltage Stability

scholarly journals Predicting the separation of time scales in a heteroclinic network

2019 ◽  
Vol 4 (1) ◽  
pp. 279-288 ◽  
Author(s):  
Maximilian Voit ◽  
Hildegard Meyer-Ortmanns
Keyword(s):  
Time Scales ◽  
Volterra Equations ◽  
Heteroclinic Cycle ◽  
Slow Oscillations ◽  
Structural Hierarchy ◽  
Branching Points ◽  
Heteroclinic Connection ◽  
Fast Oscillations ◽  
Basic Level ◽  
Heteroclinic Network

AbstractWe consider a heteroclinic network in the framework of winnerless competition, realized by generalized Lotka-Volterra equations. By an appropriate choice of predation rates we impose a structural hierarchy so that the network consists of a heteroclinic cycle of three heteroclinic cycles which connect saddles on the basic level. As we have demonstrated in previous work, the structural hierarchy can induce a hierarchy in time scales such that slow oscillations modulate fast oscillations of species concentrations. Here we derive a Poincaré map to determine analytically the number of revolutions of the trajectory within one heteroclinic cycle on the basic level, before it switches to the heteroclinic connection on the second level. This provides an understanding of which parameters control the separation of time scales and determine the decisions of the trajectory at branching points of this network.

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