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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…
Understanding how transient dynamics unfold in response to localized inputs is central to predicting and controlling signal propagation in network systems, including neural processing, epidemic intervention, and power-grid resilience.…
We derive the full set of macroscopic equations necessary to describe the dynamics of systems with active polar order in a viscoelastic or elastic background. The active polar order is manifested by a second velocity, whose non-zero modulus…
A method for the quantitative analysis of the degree and parameters of synchronization of the chaotic oscillations in two coupled oscillators is proposed, which makes it possible to reveal a change in the structure of attractors. The…
In order to analyze structure of tangent spaces of a transient orbit, we propose a new algorithm which pulls back vectors in tangent spaces along the orbit by using a calculation method of covariant Lyapunov vectors. As an example, the…
This paper studies countable systems of linearly and hierarchically interacting diffusions taking values in the positive quadrant. These systems arise in population dynamics for two types of individuals migrating between and interacting…
There is an abundance of evidence that some relaxation dynamics, e.g., exponential decays, are much more common in nature than others. Recently, there have been attempts to trace this dominance back to a certain stability of the prevalent…
The central task in the study of self-organization is to explore the general mechanism of emergences. However, this is inhibited by the missing of a full knowledge of the microscopic dynamics of emergence. Here, in this study, the…
Active agents with time-delayed interactions arise naturally in various real-world systems, such as biological systems, transportation networks and robotic swarms. Such systems are typically modeled as Delay Differential Equations (DDEs)…
In networked systems, the interplay between the dynamics of individual subsystems and their network interactions has been found to generate multistability in various contexts. Despite its ubiquity, the specific mechanisms and ingredients…
This article introduces, and reviews recent work using, a simple optimisation technique for analysing the nonlinear stability of a state in a dynamical system. The technique can be used to identify the most efficient way to disturb a system…
We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the result remain unchanged: the response can be…
In this paper, sparsity-promoting regression techniques are employed to automatically identify from data relevant triadic interactions between modal structures in large Galerkin-based models of two-dimensional unsteady flows. The approach…
In the following we consider a 2-dimensional system of ODE's containing quasiperiodic terms. The system is proposed as an extension of Mathieu-type equations to higher dimensions, with emphasis on how resonance between the internal…
The polar interface between LaAlO$_{3}$ and SrTiO$_{3}$ has shown promise as a field effect transistor, with reduced (nanoscale) feature sizes and potentially added functionality over conventional semiconductor systems. However, the…
A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…
Artificial neural networks, widely recognised for their role in machine learning, are now transforming the study of ordinary differential equations (ODEs), bridging data-driven modelling with classical dynamical systems and enabling the…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…
We study out-of-time order correlators (OTOCs) of the form $\langle\hat A(t)\hat B(0)\hat C(t)\hat D(0)\rangle$ for a quantum system weakly coupled to a dissipative environment. Such an open system may serve as a model of, e.g., a small…
We extended the Density Matrix Renormalization Group method to study the real time dynamics of interacting one dimensional spinless Fermi systems by applying the full time evolution operator to an initial state. As an example we describe…