Related papers: Monotone Systems with Inputs and Outputs

Algorithms for min-max optimization and variational inequalities are often studied under monotonicity assumptions. Motivated by non-monotone machine learning applications, we follow the line of works [Diakonikolas et al., 2021, Lee and Kim,…

In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce…

Nonlinear dynamical systems possessing an invariant subspace in the phase space and chaotic or stochastic motion within the subspace often display on-off intermittency close to the threshold of stability of the subspace. In a class of…

This paper introduces and studies the notion of output-input stability, which represents a variant of the minimum-phase property for general smooth nonlinear control systems. The definition of output-input stability does not rely on a…

This paper provides the analysis for structural and functional approaches of complex network systems research. In order to study the behavior of these systems the flow adjacency matrices were introduced, and local and global dynamic…

The asynchronous systems are the non-deterministic real time-binary models of the asynchronous circuits from electrical engineering. Autonomy means that the circuits and their models have no input. Regularity means analogies with the…

The scope of this work is to provide a self-contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems, as well as a brief survey on the main approaches to control synthesis.…

We discuss the method of folding for discrete planar systems and use it to establish the existence or non-existence of cycles or chaos in planar systems of rational difference equations with variable coefficients. These include some systems…

A generalization of the classical secant condition for the stability of cascades of scalar linear systems is provided for passive systems. The key is the introduction of a quantity that combines gain and phase information for each system in…

Nowadays, multiscale modelling is recognized as the most suitable way to study biological processes. Indeed, almost every phenomenon in nature exhibits a multiscale behaviour, i.e., it is the outcome of interactions that occur at different…

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems like the power grid, social, and neural networks, and they form the…

This work gives a mathematical study of tissue dynamics. We combine within-cell genome dynamics and diffusion between cells, where the synthesis of the two gives rise to the emergence of function. We introduce a concept of monotonicity and…

Receptor-induced apoptosis is a complex signal transduction pathway involving numerous protein/protein interactions and post-transcriptional modifications. The response to death receptor stimulation varies significantly from one cell line…

We discuss three different aspects of the quantum dynamics of bio-molecular systems and more generally complex networks in the presence of strongly coupled environments. Firstly, we make a case for the systematic study of fundamental…

Stability of power networks is an increasingly important topic because of the high penetration of renewable distributed generation units. This requires the development of advanced (typically model-based) techniques for the analysis and…

In this paper we present a method of discrete modeling and analysis of multi-level dynamics of complex large-scale hierarchical dynamic systems subject to external dynamic control mechanism. In a model each state describes parallel dynamics…

This paper is motivated by the problem of asymptotically stabilizing invariant sets in the state space of control systems by means of output feedback. The sets considered are smooth embedded in submanifolds and the class of system is…

The possibility that evolutionary forces -- together with a few fundamental factors such as thermodynamic constraints, specific computational features enabling information processing, and ecological processes -- might constrain the logic of…

While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…

We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit…