A Note on Multistability and Monotone I/O Systems
نویسندگان
چکیده
Multi-stability and hysteresis are important systems properties in many applications, and particularly in biology. This paper studies such properties in the framework of monotone systems with well-defined steady-state responses. Characterizations of global stability behavior are stated in terms of easily checkable graphical conditions.
منابع مشابه
Monotone systems under positive feedback: multistability and a reduction theorem
For feedback loops involving single input, single output monotone systems with well-defined I/O characteristics, a recent paper by Angeli and Sontag provided an approach to determining the location and stability of steady states. A result on global convergence for multistable systems followed as a consequence of the technique. The present paper extends the approach to multiple inputs and output...
متن کاملMultistability in Monotone I/O Systems, Preliminary Report
Detecting if a system is monotone with respect to the partial order induced by some positivity cone K, without actually having to compute explicit trajectories of the system itself, is of course a very important task in order to apply our results in any specific situation. Necessary and sufficient differential characterizations of monotonicity are discussed in [1], where extensions to systems w...
متن کاملA Remark on Monotone I/O Systems
This note remarks that small-gain results for a negative feedback loop around a monotone system can be seen as consequences of results concerning an extended monotone system.
متن کاملOffset-Polygon Annulus Placement Problems
r down tò 2 , it is a weakly monotone increasing function. But in a monotone function, a value can only appear once (or in one continuous range). Since the function is divided into two weakly monotone regions, a xed value can appear at most twice (or in two continuous ranges). This suuces to show that there can be at most two intersections between (I r) and O r , one in each weakly monotone reg...
متن کاملFr{'e}chet and Hausdorff Queries on $x$-Monotone Trajectories
vspace{0.2cm}In this paper, we design a data structure for the following problem. Let $pi$ be an $x$-monotone trajectory with $n$ vertices in the plane and $epsilon >0$. We show how to preprocess $pi$ and $epsilon$ into a data structure such that for any horizontal query segment $Q$ in the plane, one can quickly determine the minimal continuous fraction of $pi$ whose Fr{'e}chet and Hausdo...
متن کامل