The degree of complexity of the cortical processes related to different cognitive actions should logically produce an image in the electric and magnetic signals of the human brain. Hence, those measures of chaoticity will depend on the particular task being investigated. In many cases, the duration of a brain process does not allow for the generated signal to be treated as stationary. Therefore...

It is the aim of this paper to further the use of Lyapunov and local Lyapunov exponent methods for analyzing phenomena involving nonlinear vessel dynamics. Lyapunov exponents represent a means to measure the rate of convergence or divergence of nearby trajectories thus denoting chaos and possibly leading to the onset of conditions that produce capsize. The work developed here makes use of Lyapu...

The largest Lyapunov exponent of an ergodic Hamiltonian system is the rate of exponential growth of the norm of a typical vector in the tangent space. For an N-particle Hamiltonian system with a smooth Hamiltonian of the type p(2)+V(q), the evolution of tangent vectors is governed by the Hessian matrix V of the potential. Ergodicity implies that the Lyapunov exponent is independent of initial c...

We present a method of approximating the unique invariant measure and associated Lyapunov exponents of a random dynamical system deened by the iid composition of a family of maps in situations where only one Lyapunov exponent is observed. As a corollary, our construction also provides a method of estimating the top Lyapunov exponent of an iid random matrix product. We develop rigorous numerical...

abstract tax is one of the main sources of financing government budget. therefore, having a clear picture about the attainable amount of taxes are not only necessary for optimal allocation of scarce resources for tax collection, but also helps the government to develop precise tax collection programs .in this article, the structural features of the tax revenues series have first been examined i...

chaos theory discusses unstable and non-periodic behavior of non-linear fluctuating dynamicsystems. since evaporation level variations of lakes have a dynamic identity, chaos theory can have a uniquerole in collecting data of these variations. therefore it is an important and challenging problem in the field ofplanning and qualitative and quantitative management of urmia lake to verify whether ...

We calculate the Lyapunov exponents in a classical molecular dynamics framework. The system is composed of few hundreds particles interacting either through Yukawa (Nuclear) or Slater-Kirkwood (Atomic) forces. The forces are chosen to give an Equation of State that resembles the nuclear and the atomic 4 He Equation Of State respectively near the critical point for liquid-gas phase transition. W...

Emergent behaviors of collective intelligence systems, exemplified by swarm model, have attracted broad interests in recent years. However, current research mostly stops at observational interpretations and qualitative descriptions of emergent phenomena, and is essentially short of quantitative analysis and evaluation. In this paper, we conduct a quantitative study on the emergence of swarm mod...