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There has recently been an explosion of interest in how "higher-order" structures emerge in complex systems. This "emergent" organization has been found in a variety of natural and artificial systems, although at present the field lacks a…
We apply the formalism of dynamical system analysis to investigate the evolution of interacting dark energy scenarios at the background and perturbation levels in a unified way. Since the resulting dynamical system contains the extra…
We study the bipartite entanglement of strongly correlated systems using exact diagonalization techniques. In particular, we examine how the entanglement changes in the presence of long-range interactions by studying the Pariser-Parr-Pople…
We consider a 2-dimensional stochastic differential equation in polar coordinates depending on several parameters. We show that if these parameters belong to a specific regime then the deterministic system explodes in finite time, but the…
Entangled systems are prevalent in both biological and synthetic materials. This study examines the stable configurations of weaves consisting of two families of intertwined threads, such as warp and weft threads. By analyzing the steepest…
Thermodynamic and dynamical properties of systems with long-range pairwise interactions (LRI), which decay as $1/r^{d+\sigma}$ at large distances $r$ in $d$ dimensions, are reviewed. Two broad classes of such systems are discussed. (i)…
Dynamics in a distributed system are self-stabilizing if they are guaranteed to reach a stable state regardless of how the system is initialized. Game dynamics are uncoupled if each player's behavior is independent of the other players'…
This paper, we explore the dynamics of threshold networks on undirected signed graphs. Much attention has been dedicated to understanding the convergence and long-term behavior of this model. Yet, an open question persists: How does the…
Systems with long range interactions display some anomalies when its dynamics and thermodynamics are studied below certain conditions. Among these anomalies are the quasi- stationary states, which are exacerbated because of special initial…
The inverse problem of statistical mechanics involves finding the minimal Hamiltonian that is consistent with some observed set of correlation functions. This problem has received renewed interest in the analysis of biological networks; in…
We study long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system. Such a scenario is frequently encountered in the context of plasmas, self-gravitating systems,…
The predictability of weather and climate is strongly state-dependent: special and extremely relevant atmospheric states like blockings are associated with anomalous instability. Indeed, typically, the instability of a chaotic dynamical…
Alignment interactions in active matter are typically modeled as relaxational dynamics toward local consensus. In unbounded systems, this makes alignment effectively decoupled from local density and therefore unable to sustain self-confined…
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…
In this paper we examine the stability of scalar perturbations in nonsingular models which emerge from an interacting vacuum component. The analysis developed in this paper relies on two phenomenological choices for the energy exchange…
Diverse collective dynamics emerge in dynamical systems interacting on top of complex network architectures. Along this line of research, temporal network has come out to be one of the most promising network platforms to investigate.…
This paper answers the question if a qualitatively heterogeneous passive networked system containing damped and undamped nodes shows consensus in the output of the nodes in the long run. While a standard Lyapunov analysis shows that the…
Ecological models traditionally explain stability and coexistence through pairwise interactions among species. These interactions can also involve groups of three or more species, higher-order interactions, which recent theory suggests can…
Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…
We investigate the dynamical systems modeling conflict processes between a pair of opponents. We assume that opponents are given on a common space by distributions (probability measures) having the similar or self-similar structure. Our…