Related papers: Monotone Systems with Inputs and Outputs

Nonlinear systems driven by recurrent signals are known to exhibit complex dynamical responses which, in the physiological context, can have important functional consequences. One of the simplest biological systems that is exposed to such…

Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…

The study of biological cells in terms of mesoscopic, nonequilibrium, nonlinear, stochastic dynamics of open chemical systems provides a paradigm for other complex, self-organizing systems with ultra-fast stochastic fluctuations, short-time…

Habituation - a phenomenon in which a dynamical system exhibits a diminishing response to repeated stimulations that eventually recovers when the stimulus is withheld - is universally observed in living systems from animals to unicellular…

The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…

These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…

The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…

The theory of uninterpreted functions is a key modeling tool for systems with unknown or abstracted components. Some domains such as systems biology impose further restrictions regarding monotonicity on these components, requiring specific…

A method of optimal control computation is proposed for problems with control and state constraints. It uses a sequence of control structure adjustments in the form of generations and reductions of nodes and arcs, which do not change the…

In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…

The robust disturbance rejection controller has been the subject of intensive research due to its undeniable importance for automation. Modern control theory tends to use model-based approaches versus model-free approaches, especially when…

The interplay of positive and negative feedback loops on different time scales appears to be a fundamental mechanisms for robust and tunable oscillations in both biological systems and electro-mechanical systems. We develop a detailed…

To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…

Cellular heterogeneity is an immanent property of biological systems that covers very different aspects of life ranging from genetic diversity to cell-to-cell variability driven by stochastic molecular interactions, and noise induced cell…

Feedback optimization algorithms compute inputs to a system using real-time output measurements, which helps mitigate the effects of disturbances. However, existing work often models both system dynamics and computations in either discrete…

We present a stabilizing output-feedback controller for nonlinear finite and infinite-dimensional control systems governed by monotone operators that respects given input constraints. In particular, we show under a detectability-like…

The main focus of this paper is to study multi-valued linear monotone operators in the contexts of locally convex spaces via the use of their Fitzpatrick and Penot functions. Notions such as maximal monotonicity, uniqueness,…

A monotone function interval is the set of monotone functions that lie pointwise between two fixed monotone functions. We characterize the set of extreme points of monotone function intervals and apply this to a number of economic settings.…

We introduce and discuss the concept of modular entanglement. This is the entanglement that is established between the end points of modular systems composed by sets of interacting moduli of arbitrarily fixed size. We show that end-to-end…

The theory of mixed-feedback systems provides an effective framework for the design of robust and tunable oscillations in nonlinear systems characterized by interleaved fast positive and slow negative feedback loops. The goal of this paper…