Features Samples Cardiointervals: Chaos and Stochastics in the Description of Complex Biosystems

2015 ◽  
Vol 22 (2) ◽  
pp. 19-26
Author(s):  
Горбунов ◽  
D. Gorbunov ◽  
Синенко ◽  
D. Sinenko ◽  
Козлова ◽  
...  
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic Systems ◽  
Binary Classification ◽  
Order Parameters ◽  
Self Organization ◽  
Initial State ◽  
Diagnostic Signs ◽  
Large Groups ◽  
Complex Biosystems ◽  
Number Of Iterations

Complex Biosystems (complexity) cannot be attributed to traditional chaotic systems, because for them it is impossible to calculate the autocorrelation function, Lyapunov exponent, no run properties of mixing, continuously the state vector x(t) demonstrates chaotic motion in the form άχίάίΦθ. Since the initial state x(to) is arbitrarily unrepeatable for such systems, type-one uncertainty and type-two uncertainty arise. Type-one uncertainty is characterized by absence of statistically significant differences between samples. The authors propose neurocomputing methods and theory of chaos and self-organization to differentiate these samples. The authors present examples of such a situation for the parameters of the cardio-respiratory system of humans in conditions of the latitudinal displacement of large groups of people. It is shown that the neuroemulator not only solves the problem of binary classification, but also identifies the order parameters in diagnostic signs. It is very important to increase the number of iterations in the repetition of binary classification. The number of iteration (when we repeat the neuroemulator procedure) has the fundamental role for identification of order parameters. Errors are possible within the order parameters with the high number of iterations.

Cognitive and heuristic brain activity modeling by neural emulator

10.12737/3398 ◽  
2014 ◽  
Vol 3 (1) ◽  
pp. 62-70
Author(s):  
Еськов ◽  
Valeriy Eskov ◽  
Еськов ◽  
Valeriy Eskov ◽  
Хадарцев ◽  
...  
Keyword(s):  
Neural Network ◽  
Uniform Distribution ◽  
Decision Model ◽  
Brain Activity ◽  
Binary Classification ◽  
Order Parameters ◽  
Parameters Identification ◽  
Initial Weight ◽  
Activity Modeling ◽  
Number Of Iterations

The decision model of identification of significant diagnostic characters (order parameters) is presented within using of neural network decision model for binary classification (division of a group of subjects being in two different ecological and psychic conditions). Similar problems are the basis of cognitive and heuristic activity of a human who has to identify order parameters in any process and analysis of any events. We have shown that the possibility of order parameters identification (significant хi) is low in a small number of iterations (p<100) with initial weight characters xio based on uniform distribution (xio from an interval (0,1)). If p increases (p>100, p>1000), accuracy of order parameters identification increases too. Within the frameworks of the model there is a hypothesis on the connection of reverberation in hippocampus with efficiency of a heuristic brain activity.

scholarly journals Simulation of Human Limb Movement

2020 ◽  
pp. 32-43
Author(s):  
Dmitriy Gorbunov
Keyword(s):  
Experimental Data ◽  
Simulation Model ◽  
Chaotic Dynamics ◽  
Random Number Generation ◽  
Mathematical Statistics ◽  
Self Organization ◽  
Mathematical Form ◽  
Model Data ◽  
Initial State ◽  
Complex Biosystems

Simulation of any processes is based on some laws that take place inside the simulated object and outside it (changing the environment in which the object is located). In the study of complex biosystems, the identification of patterns is complicated by the fact that such systems have a chaotic structure. In such systems, it is impossible to arbitrarily repeat the initial state xi, any intermediate xn and final xk. Simulation of complex biosystems should be based on random patterns. The created simulation model works based on the random number generation. There are no static values in the model. The inclusion of regulatory mechanisms of the model is based on the search of F-solutions. Chaotic dynamics of changes in the trajectory of a person's limb is established based on experimental data. In accordance with this, in the simulation model, the level of limb retention in space changes its direction by random images in real time. In the framework of the above patterns, a mathematical model of the interaction of muscle bundles was developed to solve the problem of holding the limb in space. When analyzing the performance of the simulation model, the basis of the evaluation measure was taken. The results were obtained on the basis of mathematical statistics and the calculation of the quasiattractor parameters in the framework of the theory of chaos and self-organization. As a result, the correspondence of experimental and model data was established. In the framework of mathematical statistics, when constructing matrices of paired comparisons for experimental data, the number of pairs of matches (the word "matches" refers to the possibility of assigning the compared pairs of samples to one general set) is k = 11 %. The same number of coincidence pairs in percentage terms was established when comparing model data and model with experimental data. In the framework of the theory of chaos and self-organization, the quasiattractor parameters coincide in their area and visual assessment of phase planes. As a result of the research, high accuracy of the model is established, which is ensured by some chaotic dynamics of the model with chaotic selfregulation mechanisms. There are no constants in the mathematical form of the simulation model, which ensures the reproduction of N.A. Bernstein "repetition without repetition" hypothesis, which has been proven for experimental data. For theoretical biophysics, the constructed simulation model is able to provide understanding of the neuromuscular system functioning, as well as, with some complication and expansion of the algorithm, the central nervous system.

scholarly journals Lyapunov decay in quantum irreversibility

2016 ◽  
Vol 374 (2069) ◽  
pp. 20150157 ◽  
Author(s):  
Ignacio García-Mata ◽  
Augusto J. Roncaglia ◽  
Diego A. Wisniacki
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Lyapunov Exponent ◽  
Haar Measure ◽  
Chaotic Systems ◽  
Initial State ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
Dimensional Hilbert Space ◽  
Loschmidt Echo

The Loschmidt echo—also known as fidelity—is a very useful tool to study irreversibility in quantum mechanics due to perturbations or imperfections. Many different regimes, as a function of time and strength of the perturbation, have been identified. For chaotic systems, there is a range of perturbation strengths where the decay of the Loschmidt echo is perturbation independent, and given by the classical Lyapunov exponent. But observation of the Lyapunov decay depends strongly on the type of initial state upon which an average is carried out. This dependence can be removed by averaging the fidelity over the Haar measure, and the Lyapunov regime is recovered, as has been shown for quantum maps. In this work, we introduce an analogous quantity for systems with infinite dimensional Hilbert space, in particular the quantum stadium billiard, and we show clearly the universality of the Lyapunov regime.

Entropy approach in the estimation of parameters of cardio schoolboys at latitudinal

2015 ◽  
Vol 4 (2) ◽  
pp. 20-28
Author(s):  
Ястребов ◽  
A. Yastrebov ◽  
Горбунов ◽  
D. Gorbunov ◽  
Эльман ◽  
...  
Keyword(s):  
Distribution Function ◽  
Lyapunov Exponent ◽  
Chaotic Systems ◽  
Diagnostic Value ◽  
Estimation Of Parameters ◽  
Initial State ◽  
Time Intervals ◽  
Climatic Zones ◽  
Continuous State ◽  
And Performance

Options cardio demonstrate the instability of the distribution function f (x) for different time intervals of measurements Δt. We postulate that such systems can not be attributed to the traditional chaotic systems, as for them it is impossible to calculate the autocorrelation function, Lyapunov exponent, no mixing and performance properties of continuous state vector x (t) demonstrates the chaotic motion in the form dx / dt ≠ 0. Since the initial state x (t0) can not be repeated arbitrarily for such systems, there is the uncertainty of the 1st and the 2nd type. Entropy approach is proposed for describing the assessment of the behavior of cardio when changing climatic zones. Compares the value of the results of quasi-attractors samples cardio area and the values of the Shannon entropy. The examples of such a situation for the parameters of cardio groups of children at Ugra latitudinal displacements. It demonstrated that the entropy approach has a low diagnostic value in the evaluation of samples of cardio.

Discrete-Time Memristor Model for Enhancing Chaotic Complexity and Application in Secure Communication

2022 ◽  
Author(s):  
Wenhao Yan ◽  
Zijing Jiang ◽  
Qun Ding
Keyword(s):  
Fixed Points ◽  
Discrete Time ◽  
Dynamic Characteristics ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Two Dimensional ◽  
Initial State ◽  
One Dimensional ◽  
Backward Euler ◽  
Short Period

Abstract The physical implementation of continuoustime memristor makes it widely used in chaotic circuits, whereas discrete-time memristor has not received much attention. In this paper, the backward-Euler method is used to discretize TiO2 memristor model, and the discretized model also meets the three fingerprinter characteristics of the generalized memristor. The short period phenomenon and uneven output distribution of one-dimensional chaotic systems affect their applications in some fields, so it is necessary to improve the dynamic characteristics of one-dimensional chaotic systems. In this paper, a two-dimensional discrete-time memristor model is obtained by linear coupling the proposed TiO2 memristor model and one-dimensional chaotic systems. Since the two-dimensional model has infinite fixed points, the stability of these fixed points depends on the coupling parameters and the initial state of the discrete TiO2 memristor model. Furthermore, the dynamic characteristics of one-dimensional chaotic systems can be enhanced by the proposed method. Finally, we apply the generated chaotic sequence to secure communication.

MUTUAL AND SELF-COMPOUNDING OF CHAOTIC SYSTEMS

1996 ◽  
Vol 06 (04) ◽  
pp. 759-767
Author(s):  
R. SINGH ◽  
P.S. MOHARIR ◽  
V.M. MARU
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Dynamic Systems ◽  
Mantle Convection ◽  
Chaotic Systems ◽  
Compound System ◽  
Two Systems

The notion of compounding a chaotic system was introduced earlier. It consisted of varying the parameters of the compoundee system in proportion to the variables of the compounder system, resulting in a compound system which has in general higher Lyapunov exponents. Here, the notion is extended to self-compounding of a system with a real-earth example, and mutual compounding of dynamic systems. In the former, the variables in a system perturb its parameters. In the latter, two systems affect the parameters of each other in proportion to their variables. Examples of systems in such compounding relationships are studied. The existence of self-compounding is indicated in the geodynamics of mantle convection. The effect of mutual compounding is studied in terms of Lyapunov exponent variations.

TEMPORAL QUANTUM CHAOS

1999 ◽  
Vol 13 (18) ◽  
pp. 2361-2369 ◽  
Author(s):  
R. AURICH ◽  
F. STEINER
Keyword(s):  
Quantum Chaos ◽  
Chaotic Systems ◽  
Quantum Systems ◽  
Time Behavior ◽  
Classical Dynamics ◽  
Long Time Behavior ◽  
Initial State ◽  
Numerical Tests ◽  
Weyl Sum ◽  
Long Time

We study the long-time behavior of bound quantum systems whose classical dynamics is chaotic and put forward two conjectures. Conjecture A states that the autocorrelation function C(t)=<Ψ(0)|Ψ(t)> of a delocalized initial state |Ψ(0)> shows characteristic fluctuations, which we identify with a universal signature of temporal quantum chaos. For example, for the (appropriately normalized) value distribution of S~|C(t)| we predict the distribution P(S)=(π/2)Se-πS2/4. Conjecture B gives the best possible upper bound for a generalized Weyl sum and is related to the extremely large recurrence times in temporal quantum chaos. Numerical tests carried out for numerous chaotic systems confirm nicely the two conjectures and thus provide strong evidence for temporal quantum chaos.

Complex dynamic systems in students of interpreting training

2018 ◽  
Vol 13 (2) ◽  
pp. 185-207 ◽  
Author(s):  
Yanping Dong
Keyword(s):  
Dynamic Systems ◽  
Empirical Data ◽  
Self Organization ◽  
Future Research ◽  
Dynamic Systems Theory ◽  
Complex Dynamic ◽  
Initial State ◽  
Cognitive Changes ◽  
Complex Dynamic Systems ◽  
Contradictory Data

Abstract Students of interpreting training may go through drastic cognitive changes, but current empirical findings are disparate and isolated. To integrate these findings and to obtain a better understanding of interpreting training, the present article tries to reinterpret students of interpreting training as complex dynamic systems. Relying primarily on longitudinal empirical data from several existing studies, the article illustrates how the initial state of some key parameters influences the progress of the systems, how the parameters themselves evolve, and how interpreting competence develops as a result of self-organization. The hope is that a metatheoretical framework such as Dynamic Systems Theory will allow specific findings and particularistic models for interpreting training to be integrated. Moreover, this approach may allow false dichotomies in the field to be overcome and seemingly contradictory data in empirical reports to be better understood, thereby providing guidelines for future research.

A New Method Based on Lyapunov Exponent to Determine the Threshold of Chaotic Systems

2014 ◽  
Vol 511-512 ◽  
pp. 329-333
Author(s):  
Yang Liu ◽  
Xin Chun Zhang
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic Systems ◽  
Sampling Period ◽  
Qr Decomposition ◽  
Sampling Time ◽  
Duffing Equation ◽  
Experimental Results ◽  
New Method ◽  
Critical Threshold ◽  
Periodic Signals

The Duffing equation has been widely used to detect weak periodic signals. The transition threshold is the key to detect. Unfortunately, there is no effective method to determine the critical threshold. To solve this problem, a new method based on the QR decomposition to calculate Lyapunov exponent is presented. The accuracy of the algorithm will gradually improve with the sampling time increasing or the sampling period decreasing. The experimental results show that the method can determine the interval which contains the threshold, and detect the mutation acts of chaotic systems.

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