Relaxation behavior in a bistable chemical system near the unstable steady state and separatrix

1985 ◽  
Vol 83 (3) ◽  
pp. 1101-1110 ◽  
Author(s):  
Tammy Pifer ◽  
N. Ganapathisubramanian ◽  
Kenneth Showalter
Keyword(s):  
Steady State ◽  
Relaxation Behavior ◽  
Chemical System ◽  
Unstable Steady State

Analysis of chemical kinetic systems over the entire parameter space - I. The Sal’nikov thermokinetic oscillator

1988 ◽  
Vol 416 (1851) ◽  
pp. 391-402 ◽  
Keyword(s):  
Steady State ◽  
Parameter Space ◽  
Limit Cycles ◽  
Stable Limit Cycle ◽  
Chemical Kinetic ◽  
Phase Portraits ◽  
Stable Steady State ◽  
Stable Limit ◽  
Unstable Steady State ◽  
Undamped Oscillations

In this series of papers we re-examine, using recently developed techniques, some chemical kinetic models that have appeared in the literature with a view to obtaining a complete description of all the qualitatively distinct behaviour that the system can exhibit. Each of the schemes is describable by two coupled ordinary differential equations and contain at most three independent parameters. We find that even with these relatively simple chemical schemes there are regions of parameter space in which the systems display behaviour not previously found. Quite often these regions are small and it seems unlikely that they would be found via classical methods. In part I of the series we consider one of the thermally coupled kinetic oscillator models studied by Sal’nikov. He showed that there is a region in parameter space in which the system would be in a state of undamped oscillations because the relevant phase portrait consists of an unstable steady state surrounded by a stable limit cycle. Our analysis has revealed two further regions in which the phase portraits contain, respectively, two limit cycles of opposite stability enclosing a stable steady state and three limit cycles of alternating stability surrounding an unstable steady state. This latter region is extremely small, so much so that it could be reasonably neglected in any predictions made from the model.

Stabilization of an unstable steady state in a Mackey-Glass system

1995 ◽  
Vol 204 (3-4) ◽  
pp. 255-262 ◽  
Author(s):  
A. Namajūnas ◽  
K. Pyragas ◽  
A. Tamaševičius
Keyword(s):  
Steady State ◽  
Glass System ◽  
Unstable Steady State

scholarly journals Putting the Cycle Back into Business Cycle Analysis

2020 ◽  
Vol 110 (1) ◽  
pp. 1-47 ◽  
Author(s):  
Paul Beaudry ◽  
Dana Galizia ◽  
Franck Portier
Keyword(s):  
Steady State ◽  
Business Cycles ◽  
Business Cycle ◽  
Financial Frictions ◽  
Present Evidence ◽  
Strategic Complementarities ◽  
Exogenous Shocks ◽  
Unstable Steady State ◽  
Frequency Window ◽  
Business Cycle Analysis

Are business cycles mainly a response to persistent exogenous shocks, or do they instead reflect a strong endogenous mechanism which produces recurrent boom-bust phenomena? In this paper we present evidence in favor of the second interpretation and we highlight the set of key elements that influence our answer. The elements that tend to favor this type of interpretation of business cycles are (i) slightly extending the frequency window one associates with business cycle phenomena, (ii) allowing for strategic complementarities across agents that arise due to financial frictions, and (iii) allowing for a locally unstable steady state in estimation. (JEL E22, E24, E23, E44)

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