Related papers: Antagonistic interactions can stabilise fixed poin…
We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…
We study a process of pattern formation for a generic model of species anchored to the nodes of a network where local reactions take place, and that experience non-reciprocal long-range interactions, encoded by the network directed links.…
Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is stable or…
Complex systems with global interactions tend to be stable if interactions between components are sufficiently homogeneous. In biological systems, which often have small copy numbers and interactions mediated by diffusing agents, noise and…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
While interdependent systems have usually been associated with increased fragility, we show that strengthening the interdependence between dynamical processes on different networks can make them more robust. By coupling the dynamics of…
A central feature of complex systems is the relevance and entanglement of different levels of description. For instance, the dynamics of ecosystems can be alternatively described in terms of large ecological processes and classes of…
We investigate a model of high-dimensional dynamical variables with all-to-all interactions that are random and non-reciprocal. We characterize its phase diagram and show that the model can exhibit chaotic dynamics. We show that the…
Drawing inspiration from real world interacting systems we study a system consisting of two networks that exhibit antagonistic and dependent interactions. By antagonistic and dependent interactions, we mean, that a proportion of functional…
It is well known that, contrary to the autonomous case, the stability/instability of solutions of nonautonomous linear ordinary differential equations $x' = A(t) x$ is in no relation to the sign of the real parts of the eigenvalues of…
Recent theoretical studies of statistical mechanical properties of systems with long range interactions are briefly reviewed. In these systems the interaction potential decays with a rate slower than 1/r^d at large distances r in d…
Interconnected networks describe the dynamics of important systems in a wide range such as biological systems and electrical power grids. Some important features of these systems were successfully studied and understood through simplified…
When interpersonal interactions between individuals are described by the (discrete or continuous) dynamical systems, the interactions are usually assumed to be instantaneous: the rates of change of the actual states of the actors at given…
Diverse equilibrium systems with heterogeneous interactions lie at the edge of stability. Such marginally stable states are dynamically selected as the most abundant ones or as those with the largest basins of attraction. On the other hand,…
We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random directed graphs with a prescribed distribution of indegrees and outdegrees. We obtain two remarkable results for such…
In this paper, we study stabilizability of discrete-time switched linear systems where the switching signal is considered as an arbitrary disturbance (and not a control variable). We characterize feedback stabilization via necessary and…
In this letter a new solvable model of synchronization dynamics is introduced. It consists of a system of long range interacting tops with random precession frequencies. The model allows for an explicit study of orientational effects in…
We study the dynamics of a finite chain of diffusively coupled Lorenz oscillators with periodic boundary conditions. Such rings possess infinitely many fixed states, some of which are observed to be stable. It is shown that there exists a…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…