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We investigate the classical and quantum dynamics of an electron confined to a circular quantum dot in the presence of homogeneous $B_{dc}+B_{ac}$ magnetic fields. The classical motion shows a transition to chaotic behavior depending on the…

This work proposes an innovative approach using machine learning to predict extreme events in time series of chaotic dynamical systems. The research focuses on the time series of the H\'enon map, a two-dimensional model known for its…

This paper aims to theoretically prove by applying Marotto's Theorem that both transiently chaotic neural networks (TCNN) and discrete-time recurrent neural networks (DRNN) have chaotic structure. A significant property of TCNN and DRNN is…

We studied neural automata -or neurobiologically inspired cellular automata- which exhibits chaotic itinerancy among the different stored patterns or memories. This is a consequence of activity-dependent synaptic fluctuations, which…

The paper gives a systematic analysis of singularities of transition processes in dynamical systems. General dynamical systems with dependence on parameter are studied. A system of relaxation times is constructed. Each relaxation time…

A complex contagion is an infectious process in which individuals may require multiple transmissions before changing state. These are used to model behaviors if an individual only adopts a particular behavior after perceiving a consensus…

Multistability is a common phenomenon which naturally occurs in complex networks. If coexisting attractors are numerous and their basins of attraction are complexly interwoven, the long-term response to a perturbation can be highly…

One of the outstanding problems in complexity science and dynamical system theory is understanding the dynamic behavior of high-dimensional networked systems and their susceptibility to transitions to undesired states. Because of varied…

In recent years, analysis and control of quantum chaos are increasingly important, but the lack of the concept of trajectory makes it impossible to analyze quantum chaos by the methods used in classical chaos. This research aims to connect…

Many natural systems show emergent phenomena at different scales, leading to scaling regimes with signatures of chaos at large scales and an apparently random behavior at small scales. These features are usually investigated quantitatively…

We investigate the quantum chaotic properties of the Dicke Hamiltonian; a quantum-optical model which describes a single-mode bosonic field interacting with an ensemble of $N$ two-level atoms. This model exhibits a zero-temperature quantum…

We demonstrate the presence of chaos in stochastic simulations that are widely used to study biodiversity in nature. The investigation deals with a set of three distinct species that evolve according to the standard rules of mobility,…

The generalization properties of an attractive network of non monotonic neurons which infers concepts from samples are studied. The macroscopic dynamics for the overlap between the state of the neurons with the concepts, well as the…

The study of deterministic chaos continues to be one of the important problems in the field of nonlinear dynamics. Interest in the study of chaos exists both in low-dimensional dynamical systems and in large ensembles of coupled…

The presence of a nonattractive chaotic set, also called chaotic saddle, in phase space implies the appearance of a finite time kind of chaos that is known as transient chaos. For a given dynamical system in a certain region of phase space…

Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered…

We study the dynamics of an intriguing crossover from a chaotic to a power law state as a function of strain rate within the context of a recently introduced model which reproduces the crossover. While the chaotic regime has a small set of…

This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N…

We study the delocalisation transition which takes places in one-dimensional disordered systems when the random potential exhibits specific long-range correlations. We consider the case of weak disorder; using a systematic perturbative…

We demonstrate on a representative example of a planar hybrid system with digital sampling a sudden transition from a stable limit cycle to the onset of chaotic dynamics. We show that the scaling law in the size of the attractor is…