Related papers: Detection of chaotic behavior in time series
Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…
Dynamical chaos is a fundamental manifestation of gravity in astrophysical, many-body systems. The spectrum of Lyapunov exponents quantifies the associated exponential response to small perturbations. Analytical derivations of these…
Nonlinear dynamics (``chaos theory'') and quantum mechanics are two of the scientific triumphs of the 20th century. The former lies at the heart of the modern interdisciplinary approach to science, whereas the latter has revolutionized…
This paper focuses on an interesting phenomenon when chaos meets computers. It is found that digital computers are absolutely incapable of showing true long-time dynamics of some chaotic systems, including the tent map, the Bernoulli shift…
Chaos is associated with stochasticity, complex, irregular motion, etc. It has some peculiar properties such as ergodicity, highly initial value sensitivity, non-periodicity and long-term unpredictability. These pseudo random features lead…
Chaos is an intriguing phenomenon that can be found in an immense variate of systems. Its detection and discrimination from its counterpart order poses an interesting challenge. To address it, we present a deep classifier capable of…
In this paper we propose an application of adaptive synchronization of chaos to detect changes in the topology of a mobile robotic network. We assume that the network may evolve in time due to the relative motion of the mobile robots and…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order…
Herding defines a deterministic dynamical system at the edge of chaos. It generates a sequence of model states and parameters by alternating parameter perturbations with state maximizations, where the sequence of states can be interpreted…
The paper is focused on the discussion of the phenomenon of transitional chaos in dynamic autonomous and non-autonomous systems. This phenomenon involves the disappearance of chaotic oscillations in specific time periods and the system…
As cities around the world aim to improve walkability and safety, understanding the irregular and unpredictable nature of pedestrian behavior has become increasingly important. This study introduces a data-driven framework for modeling…
We propose a simple method to estimate the parameters involved in discrete dynamical systems from time series. The method is based on the concept of controlling chaos by constant feedback. The major advantages of the method are that it…
We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…
Adaptive dynamical networks are network systems in which the structure co-evolves and interacts with the dynamical state of the nodes. We study an adaptive dynamical network in which the structure changes on a slower time scale relative to…
Chaos is usually referred to the sensitivity to initial conditions in which the nonlinearity plays a crucial role. Beyond such a mathematical description, the understanding of the underlying physical origin of the chaos is still not very…
Chaos and nonlinear economic dynamics are addressed for a quantum coupled map lattice model of an artificial economy, with quantized supply and demand equilibrium conditions. The measure theoretic properties and the patterns that emerge in…
A nonuniform system is considered consisting of two phases with different densities of particles. At each given time the distribution of the phases in space is chaotic: each phase filling a set of regions with random shapes and locations. A…
Due to the deterministic nature of chaotic systems, fluctuations in their trajectories arise solely from the choice of initial conditions. Some of these dynamical fluctuations may lead to extremely unlikely scenarios. Understanding the…
Modern computer microprocessors are composed of hundreds of millions of transistors that interact through intricate protocols. Their performance during program execution may be highly variable and present aperiodic oscillations. In this…