The dynamics of dissipative and coherent N-body systems, such as a Bose–Einstein condensate, which can be described by an extended Gross–Pitaevskii formalism, is investigated. In order to analyze chaotic and unstable regimes, two approaches are considered: a metric one, based on calculations...

Tangent bifurcations in maps with type-I intermittency have been studied numerically and oscillations in the statistical properties were found as functions of the control parameter. The average length of laminar events, the Lyapunov exponent and the averages of the dynamical variable were...

Time complexity is associated with sensitive dependence on initial conditions and severe intrinsic predictability limits, in particular, the ‘butterfly effect’ paradigm: an exponential error growth and a corresponding characteristic predictability time. This was believed to be the universal...

Price changes in financial data fluctuate irregularly or stochastically. This paper investigates whether the irregular fluctuations are random or have some kind of dynamics by applying a recently developed method, the small-shuffle surrogate method. The data used are daily gold price, daily...

Non-extensive thermodynamics is one of the most intriguing physics new frontiers. A large number of researchers have been successfully finding connections between the new concepts introduced by this new field and other complex systems already presented. In particular, Borland [Phys. Rev. E 57...

We propose a method from the viewpoint of deterministic dynamical systems to investigate whether observed data follow a random walk (RW) and apply the method to several financial data. Our method is based on the previously proposed small-shuffle surrogate method. Hence, our method does not...

Price dynamics is analyzed in terms of a model which includes the possibility of effective forces due to trend followers or trend adverse strategies. The method is tested on the data of a minority–majority model and indeed it is capable of reconstructing the prevailing traders’ strategies in...

We consider the role of finite size effects on the value of the effective Hurst exponent H. This problem is motivated by the properties of the high-frequency daily stock-prices. For a finite size random walk we derive some exact results based on Spitzer's identity. The conclusion is that finite...

Financial data usually show irregular fluctuations and some trends. We investigate whether there are correlation structures in short-term variabilities (irregular fluctuations) among financial data from the viewpoint of deterministic dynamical systems. Our method is based on the small-shuffle...

The possibility that price dynamics is affected by its distance from a moving average has been recently introduced as new statistical tool. The purpose is to identify the tendency of the price dynamics to be attractive or repulsive with respect to its own moving average. We consider a number of...