Related papers: Qualitative stability of nonlinear networked syste…
Stability of the zero solution plays an important role in the investigation of positive systems. In this note, we revisit the $\mu$-stability of positive nonlinear systems with unbounded time-varying delays. The system is modelled by…
The problem of the dynamical stability of anistropic systems is studied, by proposing a criterion in terms of the adiabatic local index $\gamma$. The result has general validity and can be applied to several physical situations.…
It is shown that a positive linear system on a time scale with a bounded graininess is uniformly exponentially stable if and only if the characteristic polynomial of the matrix defining the system has all its coefficients positive. Then…
The principle of linearized stability is established for age-structured diffusive populations incorporating nonlinear death and birth processes. More precisely, asymptotic exponential stability is shown for equilibria for which the…
Species or population that proliferate faster than others become dominant in numbers. Catalysis allows catalytic sets within a molecular reaction network to dominate the non catalytic parts of the network by processing most of the available…
It is well known that, for mass-action systems, complex-balanced equilibria are asymptotically stable. For generalized mass-action systems, even if there exists a unique complex-balanced equilibrium (in every stoichiometric class and for…
Generalized mass-action systems are power-law dynamical systems arising from chemical reaction networks. Essentially, every nonnegative ODE model used in chemistry and biology (for example, in ecology and epidemiology) and even in economics…
The central theme of complex systems research is understanding the emergent macroscopic properties of a system from the interplay of its microscopic constituents. Here, we ask what conditions a complex network of microscopic dynamical units…
This work deals with a scalar nonlinear neutral delay differential equation issued from the study of wave propagation. A critical value of the coefficients is considered, where only few results are known. The difficulty follows from the…
The consensus that complexity begets stability in ecosystems was challenged in the seventies, a result recently extended to ecologically-inspired networks. The approaches assume the existence of a feasible equilibrium, i.e. with positive…
This paper derives two stabilizability theorems for a basic class of discrete-time nonlinear systems with multiple unknown parameters. First, we claim that a discrete-time multi-parameter system is stabilizable if its nonlinear growth rate…
We study nonlinear dynamics on complex networks. Each vertex $i$ has a state $x_i$ which evolves according to a networked dynamics to a steady-state $x_i^*$. We develop fundamental tools to learn the true steady-state of a small part of the…
The main result relates to structured robust stability analysis of an input-output model for networks with link uncertainty. It constitutes a collection of integral quadratic constraints, which together imply robust stability of the…
This paper presents an algebraic framework to study sign-sensitivities for reaction networks modeled by means of systems of ordinary differential equations. Specifically, we study the sign of the derivative of the concentrations of the…
Motivated by biochemical reaction networks, a generalization of the classical secant condition for the stability analysis of cyclic interconnected commensurate fractional-order systems is provided. The main result presents a sufficient…
Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multistationarity for a polynomial dynamical system is an…
We formulate general rules for a coarse-graining of the dynamics, which we term `symbolic dynamics', of feedback networks with monotone interactions, such as most biological modules. Networks which are more complex than simple cyclic…
This paper deals with the global stability of time-delayed dynamical networks. We show that for a time-delayed dynamical network with non-distributed delays the network and the corresponding non-delayed network are both either globally…
We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the…
Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…