Related papers: A scaling law chaotic system
We study the Kondo effect in quantum dots in an out-of-equilibrium state due to an applied dc-voltage bias. Using the method of infinitesimal unitary transformations (flow equations), we develop a perturbative scaling picture that naturally…
In this paper, we present a unified framework of multiple attractors including multistability, multiperiodicity and multichaos. Multichaos, which means that the chaotic solution of a system lies in different disjoint invariant sets with…
Examples of one-dimensional lattice systems are considered, in which patterns of different spatial scales arise alternately, so that the spatial phase over a full cycle undergo transformation according to expanding circle map that implies…
In many real world chaotic systems, the interest is typically in determining when the system will behave in an extreme manner. Flooding and drought, extreme heatwaves, large earthquakes, and large drops in the stock market are examples of…
This paper explores the chaotic properties of an advection system expressed in difference equations form. In the beginning the Aref's blinking vortex system is examined. Then several new lines are explored related to the sink problem (one…
We consider an autonomous system constructed as modification of the logistic differential equation with delay that generates successive trains of oscillations with phases evolving according to chaotic maps. The system contains two feedback…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
The dynamics of unidirectionally coupled chaotic Lorenz systems is investigated. It is revealed that chaos is present in the response system regardless of generalized synchronization. The presence of sensitivity is theoretically proved, and…
Chaotic bursting behaviors have been observed by many authors in neural dynamics mainly in the transition between different kinds of bursting behavior. As a well-known three-dimensional ODEs model with various bursting solutions, the…
It is demonstrated that decimation of the one dimensional Ising model, with periodic boundary conditions, results in a non-linear renormalisation transformation for the couplings which can lead to chaotic behaviour when the couplings are…
A multidimensional chaos is generated by a special initial value problem for the non-autonomous impulsive differential equation. The existence of a chaotic attractor is shown, where density of periodic solutions, sensitivity of solutions…
An investigation of the mesoscopic dynamics of chemical systems whose mass action equation gives rise to a deterministic chaotic attractor is carried out. A reactive lattice-gas model for the three-variable autocatalator is used to provide…
This study delves into the realm of chaotic dynamics derived from Dirichlet L-functions, drawing inspiration from Yitang Zhang's groundbreaking work on Landau-Siegel zeros. The dynamic behavior reveals profound chaos, corroborated by the…
We discover strange nonchaotic attractor (SNA) through experiments in an unforced system comprising turbulent reactive flow. While models suggest SNAs are common in dynamical systems, experimental observations are primarily limited to…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
We present a theory for Coulomb drag between two mesoscopic systems. Our formalism expresses the drag in terms of scattering matrices and wave functions, and its range of validity covers both ballistic and disordered systems. The…
The so-called chaotic states that emerge on the model of $XY$ interacting on regular critical range networks are analyzed. Typical time scales are extracted from the time series analysis of the global magnetization. The large spectrum…
The dynamical status of isolated quantum systems, partly due to the linearity of the Schrodinger equation is unclear: Conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation --…
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 paper presents two interesting scaling laws, which relate some critical exponents in the critical behavior of spherically symmetric gravitational collapses. These scaling laws are independent of the details of gravity theory under…