Oscillations in multi-stable monotone systems with slowly varying feedback
نویسندگان
چکیده
منابع مشابه
Oscillations in multi-stable monotone systems with slowly varying feedback.
The study of dynamics of gene regulatory networks is of increasing interest in systems biology. A useful approach to the study of these complex systems is to view them as decomposed into feedback loops around open loop monotone systems. Key features of the dynamics of the original system are then deduced from the input-output characteristics of the open loop system and the sign of the feedback....
متن کاملOscillations in Monotone Systems with a Negative Feedback
We study a finite-dimensional monotone system coupled to a slowly evolving scalar differential equation which provides a negative feedback to the monotone system. We use a theory of multivalued characteristics to show that this system admits a relaxation periodic orbit if a simple model system in R does. Our construction can be used to prove the existence of periodic orbits in slow-fast systems...
متن کاملOn Non-linear Oscillations with Slowly Varying System Parameters
The paper deals with an approximate analysis of non-linear oscillation problems with slowly varying system parameters. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by using the generalized averaging method of Sinha and Srinivasan based on ultraspherical polynomial expansions. The Bogoliubov-Mitro...
متن کاملNon-monotone systems decomposable into monotone systems with negative feedback
Motivated by the work of Angeli and Sontag [1] and Enciso and Sontag [7] in control theory, we show that certain finite and infinite dimensional semi-dynamical systems with “negative feedback” can be decomposed into a monotone “open loop” system with “inputs” and a decreasing “output” function. The original system is reconstituted by “plugging the output into the input”. Employing a technique o...
متن کاملIdentifiability of Slowly Varying Systems
A system is conceived of as being slowly varying if it changes slowly enough to permit identification to within a specified error. A generic model is developed to study the identifiability and identification of slowly varying systems. The model is suitable for a large variety of nonlinear, time-varying, causal, bounded memory systems; it has finitely many parameters and is linear in its paramet...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2007
ISSN: 0022-0396
DOI: 10.1016/j.jde.2007.05.029