Homeostatic System Can Not Be Described by Stochastics or Deterministic Chaos

2015 ◽  
Vol 22 (4) ◽  
pp. 28-33 ◽  
Author(s):  
Полухин ◽  
V. Polukhin ◽  
Еськов ◽  
V. Eskov ◽  
Эльман ◽  
...  

The living systems (complexity, homeostatic systems) are a special systems of the third type of complexity in natural science and for such systems it is impossible to determine the stationary state in form of dx/dt=0 (deterministic approach) or in the form of invariance of distribution function f(x) for samples acquired in a row of, the any component xi of all vectors of state x=x(t) =(x1,x2,…,xm)T in m‐dimensional phase space of states. At the same time the mixing property doesn’t met (no invariant measures), the autocorrelation functions A(t) don’t tend to zero if t→∞, Lyapunov’s constants can continuously change the sign. Such systems of the third type (complexity) do not meet the condition of Glansdorff – Prigogine’s theorem, i.e. P ‐ the rate of increase of entropy E (P=dE/dt) doesn’t minimized near the point of maximum entropy E (i.e., at point of thermodynamic equilibrium). It is proposed to use the concept of quasi‐attractors to describe the complexity.

2015 ◽  
Vol 4 (2) ◽  
pp. 65-74
Author(s):  
Гавриленко ◽  
T. Gavrilenko ◽  
Еськов ◽  
Valeriy Eskov ◽  
Еськов ◽  
...  

There are several criteria in science for stationarity (stability) of different dynamical systems. The stationarity in physics, engineering and chemistry is being interpreted as matching the requirements of dx/dt=0, where x=x(t) - is the vector of system’s state, or the equality of distribution functions f(x) for different samples which characterize the system. However, in case of social or biological systems the matching of the requirements is impossible and there is a problem of specific assessment of stationary regimes of complex systems of the third type. The possibility of studying of such systems within the frame of deterministic chaos, stochastic approach and theory of chaos and self-organization is being discussed. This article explains why I.R. Prigogine refused from materialistic (in fact deterministic) approach in the description of such special systems of third type and tried to get away from the traditional science in the description of biological systems.


10.12737/7652 ◽  
2014 ◽  
Vol 3 (4) ◽  
pp. 47-62 ◽  
Author(s):  
Еськов ◽  
V. Eskov ◽  
Джумагалиева ◽  
L. Dzhumagalieva ◽  
Филатова ◽  
...  

The main problem of modern science is pointed out: reality of specific three-type systems (TTS) that are usually presented as complexity, and simultaneously impossibility of a description of such systems by a traditional modern reducing approach. Studying properties of system elements cannot help in a description of a complex system itself – complexity (three-type systems, living systems). Hence there arises an acute need in creation of new theories which would operate with maximum uncertainty and unpredictability and provide modeling TTS. The first step in this direction was taken on the grounds of a creation of theory of chaos and self-organization (TCS), according to which complexity cannot repeat an initial state of a system (or a vector parameters x(t0)), measures are not invariant, autocorrelation functions do not converge to zero and Lyapunov exponents are not positive. Chaos of TTS differs from a deterministic chaos and statistical distribution functions f(x) are not appropriate to describe it, because they continuously change. Deterministic, stochastic and chaotic models cannot describe TTS. This is the main property of emergent systems (complexity, TTS), therefore they are described by quasi-attractors.


1979 ◽  
Vol 14 (1) ◽  
pp. 89-109
Author(s):  
B. Coupal ◽  
M. de Broissia

Abstract The movement of oil slicks on open waters has been predicted, using both deterministic and stochastic methods. The first method, named slick rose, consists in locating an area specifying the position of the slick during the first hours after the spill. The second method combines a deterministic approach for the simulation of current parameters to a stochastic method simulating the wind parameters. A Markov chain of the first order followed by a Monte Carlo approach enables the simulation of both phenomena. The third method presented in this paper describes a mass balance on the spilt oil, solved by the method of finite elements. The three methods are complementary to each other and constitute an important point for a contingency plan.


1883 ◽  
Vol 29 (125) ◽  
pp. 111-117
Author(s):  
B. F. C. Costelloe

During the long period embraced in the present Retrospect, the most important incident that has happened in the philosophical circles of this country is the death of Professor T. H. Green, of Oxford—a man who for many years had been silently acquiring, not only by his power of thinking but by his strong and blameless personal character, a marked position and a unique influence among the leaders of thought in England. His philosophical position would perhaps best be defined by saying that he became the chief of that small, but notable, band of speculative students, centred mainly in Oxford, Glasgow, and Edinburgh, who are reviving the spirit of the systems of Kant and Hegel, in its application to the new scientific, political, and religious problems of the day. His distinguishing characteristics were his modesty and his earnest sense of duty—qualities perhaps not so conspicuous as they might be amongst the better known of modern psychologists. His modesty was such that he never assumed that he had mastered the secret of any writer, until he had bestowed the most extravagant labour and thought in exploring difficulties and obscurities on which the man himself had probably never bestowed a second thought. His earnestness was so thorough that he believed it to be merely his duty to struggle with the fundamental questions of the Sphinx of modern criticism, and find for himself and others not a negative but a constructive answer, no matter what toil and trouble it might cost. For he held that those who contribute, as we all in some way do, to the formation of public opinion upon the vital subjects of life and conduct, are under a terrible responsibility if they mislead their neighbours, or even if they refuse by sloth or vanity or cynicism that healthy guidance which their own attainments would enable them to give. These remarks are suggested by the fact that the first article of the April number of “Mind” is from Prof. Green's pen. Indeed it is one of the last pieces of work he ever personally sent to press; although we are glad to know that the groat Ethical work on which he had long been engaged is left with his philosophical friends in so complete a form that it will be published immediately. The April article is the second of three essays on the question, “Can there be a natural science of man?” of which the third holds the leading place in the July number. The scope of the essays, as well as of the “Prolegomena to Ethics,” to which they were in a sense introductory, will be best indicated if we quote a note added in the July number by Prof. Green's literary executor, Mr. A. C. Bradley.


2021 ◽  
Vol 157 (7) ◽  
pp. 1610-1651
Author(s):  
Pascal Autissier ◽  
Dante Bonolis ◽  
Youness Lamzouri

In this paper, we investigate the distribution of the maximum of partial sums of families of $m$ -periodic complex-valued functions satisfying certain conditions. We obtain precise uniform estimates for the distribution function of this maximum in a near-optimal range. Our results apply to partial sums of Kloosterman sums and other families of $\ell$ -adic trace functions, and are as strong as those obtained by Bober, Goldmakher, Granville and Koukoulopoulos for character sums. In particular, we improve on the recent work of the third author for Birch sums. However, unlike character sums, we are able to construct families of $m$ -periodic complex-valued functions which satisfy our conditions, but for which the Pólya–Vinogradov inequality is sharp.


1976 ◽  
Vol 13 (3) ◽  
pp. 628-632 ◽  
Author(s):  
Ronald W. Wolff ◽  
Charles W. Wrightson

A two-server loss system is considered with N classes of Poisson arrivals, where the service distribution function and server preferences are arrival-class dependent. The stationary state probabilities are derived and found to be independent of the form of the service distributions.


2015 ◽  
Vol 4 (1) ◽  
pp. 31-39
Author(s):  
Берестин ◽  
D. Berestin ◽  
Игуменов ◽  
D. Igumenov ◽  
Рассадина ◽  
...  

The results of the stochastic analysis of postural tremor (as alleged involuntary movement) and tapping (as supposedly voluntary movement) are considered in a comparative perspective. It is proved that the stochastic analysis of the results of chaotic dynamics in tremorogramms and tapping does not give significant differences (absence of voluntariness). Typically, all samples are significantly different and it is impossible to distinguish subjects in their tremorogramms or tapingramm. The significant differences between sites of tremorogramms in terms of a normal distribution or a non-parametric distribution are demonstrated. A continuous variation of the distribution function is observed: parametric distribution shifts to non-parametric distribution, but among themselves they (distribution function) are all different. It is well known that the unpredicta-bility and continuing changes in the state are characteristic feature of chaos. The evidence of special kind of chaos in biosystems which differs significantly from the deterministic chaos of Tom – Ar-nold is given.


10.12737/6722 ◽  
2014 ◽  
Vol 3 (3) ◽  
pp. 39-46
Author(s):  
Еськов ◽  
V. Eskov

Advances in molecular biology and biophysics (at molecular-cellular level) do not contribute to understanding of life phenomena. Achievements of synergetics (H. Haken) and complexity theory (I. Prigogine) have intensified differences between physical-chemical understandings of life and systemic understandings. In addition to that, the systems approach provides the understanding of effects of living objects and especially its more organized and evolving part – human and humanity. Human-scaled systems possess the unique property – continuous and chaotic movement of many components of a system state vector x= x(t). Taking this property into consideration causes the denial of any known types of stationary nodes (for example, dx/dt=0) and requires reconsideration of concept of chaos. A novel approach for understanding of living systems (as the third paradigm of natural science) and novel methods of studying of living systems (as theory of chaos and self-organization) are proposed by the third paradigm and theory of chaos and self-organization.


1968 ◽  
Vol 5 (1) ◽  
pp. 203-209 ◽  
Author(s):  
V. E. Beneš

In the study of dynamical systems perturbed by noise, it is important to know whether the stochastic process of interest has a stationary distribution. Four necessary and sufficient conditions are formulated for the existence of a finite invariant measure for a Feller process on a σ-compact metric (state) space. These conditions link together stability notions from several fields. The first uses a Lyapunov function reminiscent of Lagrange stability in differential equations; the second depends on Prokhorov's condition for sequential compactness of measures; the third is a recurrence condition on the ergodic averages of the transition operator; and the fourth is analogous to a condition of Ulam and Oxtoby for the nonstochastic case.


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