Monotone Dynamical Systems

Monotone dynamical systems , graphs , and stability of large - scale interconnected systems

Monotone dynamical systems, graphs, and stability of large-scale interconnected systems To my parents, Antje and Herbert.

Remarks on random dynamical systems with inputs and outputs and a small-gain theorem for monotone RDS

This note introduces a new notion of random dynamical systems with inputs and outputs, and sketches a small-gain theorem for monotone systems which generalizes a similar theorem known for deterministic systems.

Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation Cycles

The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are important features of many systems, since they are required for adaptation and precision. This paper shows that, provided that these negative loops act at a comp...

Dynamical Systems Gradient method for solving nonlinear equations with monotone operators

A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new stopping rule. Numerical experiments show that the proposed stopping rule is efficient. Equations with monotone operators are of interest in many application...

A Remark On M.W. Hirsch's Paper "Chain Transitive Sets For Smooth Strogly Monotone Dynamical Systems"

Monotone control systems

Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary first step in trying to understand interconnections, especially including feedback loops, built up out of monotone components. Basic definitions and theorems a...