Related papers: Chaos in high-dimensional dynamical systems with t…
Attractors in asymmetric neural networks with deterministic parallel dynamics were shown to present a "chaotic" regime at symmetry eta < 0.5, where the average length of the cycles increases exponentially with system size, and an…
In this paper we present a hierarchical multi-rate control architecture for nonlinear autonomous systems operating in partially observable environments. Control objectives are expressed using syntactically co-safe Linear Temporal Logic…
We propose a general strategy for feedback control design of complex dynamical systems exploiting the nonlinear mechanisms in a systematic unsupervised manner. These dynamical systems can have a state space of arbitrary dimension with…
We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when…
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…
Random neural networks are dynamical descriptions of randomly interconnected neural units. These show a phase transition to chaos as a disorder parameter is increased. The microscopic mechanisms underlying this phase transition are unknown,…
We consider a nonlinear autonomous system of $N\gg 1$ degrees of freedom randomly coupled by both relaxational ('gradient') and non-relaxational ('solenoidal') random interactions. We show that with increased interaction strength such…
Metastability, i.e., partial relaxation to long-lived, quasi-stationary states before true asymptotic equilibrium sets in, emerges ubiquitously in classical and quantum dynamical systems as a result of timescales separation. In open quantum…
In the context of chaotic dynamical systems with exponential divergence of nearby trajectories in phase space, hyperchaos is defined as a state where there is divergence or stretching in at least two directions during the evolution of the…
Chaotic instability in many-body systems is commonly quantified by the largest Lyapunov exponent, yet general constraints on its magnitude in classical interacting systems remain poorly understood. Here we establish explicit,…
The essential properties of the half-filled interacting Kane-Mele model on a hexagon lattice is studied using the slave rotor approach. It is shown clearly that a long-range charge-order state with spontaneously broken chiral symmetry…
We observe the occurrence of a strange nonchaotic attractor in a periodically driven two-dimensional map, formerly proposed as a neuron model and a sequence generator. We characterize this attractor through the study of the Lyapunov…
This article presents a modeling framework for a class of multiphase chemical systems based on non-equilibrium thermodynamics. Compartmental modeling is used to establish the dynamic properties of liquid-vapor systems operating far from…
We demonstrate that a weakly disordered metal with short-range interactions exhibits a transition in the quantum chaotic dynamics when changing the temperature or the interaction strength. For weak interactions, the system displays…
This paper investigates the complex dynamics and fractal attractors that arise in a 60-dimensional ring lattice system of electrically coupled nonchaotic Rulkov neurons. While networks of chaotic Rulkov neurons have been widely studied,…
We study the dynamical properties of the canonical ordered phase of the Hamiltonian mean-field (HMF) model, in which $N$ particles, globally-coupled via pairwise attractive interactions, form a rotating cluster. Using a combination of…
Parametric modulation in nonlinear dynamical systems can give rise to attractors on which the dynamics is aperiodic and nonchaotic, namely with largest Lyapunov exponent being nonpositive. We describe a procedure for creating such…
This research investigates the dynamics of a forced Lienard oscillator featuring asymmetric potential wells. We provide compelling evidence of extreme events (EE) in the system by manipulating the height of the potential well. In the case…
This paper is concerned with the dynamics of an infinite-dimensional gradient system under small almost periodic perturbations. Under the assumption that the original autonomous system has a global attractor given as the union of unstable…
A one dimensional classically chaotic spin chain with asymmetric coupling and two different inter-spin interactions, nearest neighbors and all-to-all, has been considered. Depending on the interaction range, dynamical properties, as…