Related papers: A robust Lyapunov criterion for non-oscillatory be…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
Local bifurcation analysis plays a central role in understanding qualitative transitions in networked nonlinear dynamical systems, including dynamic neural network and opinion dynamics models. In this article we establish explicit bounds of…
In this paper, we study extinction in dynamical systems generated by reaction networks. We introduce two notions: weak extinction and strong extinction, and relate them to the structure of the underlying network through Lyapunov functions…
Lyapunov functions provide a tool to analyze the stability of nonlinear systems without extensively solving the dynamics. Recent advances in sum-of-squares methods have enabled the algorithmic computation of Lyapunov functions for…
We analyse the asymptotic behaviour of integro-differential equations modelling $N$ populations in interaction, all structured by different traits. Interactions are modelled by non-local terms involving linear combinations of the total…
Non-reciprocal interactions are a defining feature of many complex systems, biological, ecological, and technological, often pushing them far from equilibrium and enabling rich dynamical responses. These asymmetries can arise at multiple…
Biochemical oscillations are ubiquitous in nature and allow organisms to properly time their biological functions. In this paper, we consider minimal Markov state models of nonequilibrium biochemical networks that support oscillations. We…
We present a systematic mathematical analysis of the qualitative steady-state response to rate perturbations in large classes of reaction networks. This includes multimolecular reactions and allows for catalysis, enzymatic reactions,…
Using simple kinematics, we propose a general theory of linear wave interactions between the interfacial waves of a two dimensional (2D), inviscid, multi-layered fluid system. The strength of our formalism is that one does not have to…
Neural network controllers have the potential to improve the performance of feedback systems compared to traditional controllers, due to their ability to act as general function approximators. However, quantifying their safety and…
While there has been increasing interest in using neural networks to compute Lyapunov functions, verifying that these functions satisfy the Lyapunov conditions and certifying stability regions remain challenging due to the curse of…
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…
This paper investigates the problem of synchronization for nonlinear systems. Following a Lyapunov approach, we firstly study global synchronization of nonlinear systems in canonical control form with both distributed…
Organisms often use cyclic changes in the concentrations of chemicals species to precisely time biological functions. Underlying these biochemical clocks are chemical reactions and transport processes, which are inherently stochastic.…
The development of chemical reaction models aids understanding and prediction in areas ranging from biology to electrochemistry and combustion. A systematic approach to building reaction network models uses observational data not only to…
Piecewise-Linear in Rates (PWLR) Lyapunov functions are introduced for a class of Chemical Reaction Networks (CRNs). In addition to their simple structure, these functions are robust with respect to arbitrary monotone reaction rates, of…
Estimating the Region of Attraction (RoA) for nonlinear dynamical systems is a fundamental problem in control theory, with direct implications for stability analysis and safe controller design. Traditional approaches rely on analytically…
Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…
Multi-agent systems in biology, society, and engineering are capable of making decisions through the dynamic interaction of their elements. Nonlinearity of the interactions is key for the speed, robustness, and flexibility of multi-agent…
In this paper, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non necessarily small perturbations. We show that, under some estimates…