Identification of fast-changing signals by means of adaptive chaotic transformations

Abstract

The adaptive approach of strongly non-linear fast-changing signals identification is discussed. The approach is devised by adaptive sampling based on chaotic mapping "in yourself" of a signal. Presented sampling way may be utilized online in the automatic control of chemical reactor (throughout identification of concentrations and temperature oscillations in real-time), in medicine (throughout identification of ECG and EEG signals in real-time), etc. In this paper, we presented it to identify the Weierstrass function and ECG signal.

Approximate finite-dimensional ODE temperature model for microwave heating

“…As an illustration, they can be regarded as constant because of the small variation of the physical characteristics with temperature. Thus, thermodynamic parameters, such as, density ρ, specific heat C p and heat conductivity κ, can be equaled with 1 g/cm 3 In order to analyze the validity of above proposed finite-dimensional nonlinear model, we choose three points which are located in 0.37 cm, 0.71 cm and 1.11 cm, respectively, to contrast the trend of temperature rising with the closed-form solutions from traditional numerical model (8)- (10), which is used FEM. And the estimating temperatures by different models in different positions are shown in Fig.…”

“…To solve these problems, the research efforts focus on applying an auxiliary function to achieve a more complicated equivalent PDE, including not only the states of microwave irradiation and heat transfer, but also the information of boundary conditions. In this case, the Galerkin's method is applied to partition the infinite-dimensional model into a finitedimensional slow complement and an infinite-dimensional stable fast one [3,6,7,10,15], where the slow (finite-dimensional) model can also approximately describe the dynamic performance for temperature rise.…”

On the Complex and Chaotic Dynamics of Standard Logistic Sine Square Map

“…In nature, chaos is a nonlinear phenomena of nonlinear dynamical systems which is unpredictable, aperiodic and extreme sensitive on initial values [1,2]. There is diversity of fields in which chaotic maps and fractals are widely studied [3,4,5,6,7,8,9,10].…”

The problem of the inverse Lyapunov exponent and its applications

“…An interesting function for which the Lyapunov exponent also increases indefinitely, is the so called Weierstrass recurrence given as [7,17] x…”