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  • 1
    Electronic Resource
    Electronic Resource
    A terminal dynamics model of the heartbeat (1996)
    Springer
    Biological cybernetics 75 (1996), S. 277-280 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract.  It is widely assumed that heartbeat dynamics are chaotic, although there has been no evidence confirming such an opinion, and some evidence to the contrary. Additionally, the deterministic assumptions of such dynamics cannot be demonstrated. An alternative model is presented based upon the notion of terminal dynamics, which can more faithfully represent key features of the heartbeat: namely, piecewise determinism, and singular points between beats, which allow for adaptability while maintaining stability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004220050294
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  • 2
    Electronic Resource
    Electronic Resource
    A Markovian formalization of heart rate dynamics evinces a quantum-like hypothesis (1996)
    Springer
    Biological cybernetics 74 (1996), S. 181-187 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract Most investigations into heart rate dynamics have emphasized continuous functions, whereas the heart beat itself is a discrete event. We present experimental evidence that by considering this quality, the dynamics may be appreciated as a result of singular dynamics arising out of non-Lipschitz formalisms. Markov process analysis demonstrates that heart beats may then be considered in terms of quantum-like constraints.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00204206
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  • 3
    Electronic Resource
    Electronic Resource
    A Markovian formalization of heart rate dynamics evinces a quantum-like hypothesis (1996)
    Springer
    Biological cybernetics 74 (1996), S. 181-187 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract.  Most investigations into heart rate dynamics have emphasized continuous functions, whereas the heart beat itself is a discrete event. We present experimental evidence that by considering this quality, the dynamics may be appreciated as a result of singular dynamics arising out of non-Lipschitz formalisms. Markov process analysis demonstrates that heart beats may then be considered in terms of quantum-like constraints.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004220050230
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  • 4
    Electronic Resource
    Electronic Resource
    Dynamics of Intelligent Systems (2000)
    Springer
    International journal of theoretical physics 39 (2000), S. 2107-2140 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Recent advances in nonlinear dynamics demonstrate a remarkable complexity ofpatterns outside of equilibrium, which are derived from simple basic laws ofphysics. A class of mathematical models has been identified providing a varietyof such patterns in the form of static, periodic, or chaotic attractors. These modelsappear to be so general that they predict not only physical, but also biological,economic, and social patterns of behavior. Such a phenomenological reductionismmay suggest that, on the dynamical level of description, there is no differencebetween a solar system, a swarm of insects, and a stock market. However, thisconclusion is wrong for a very simple reason: Even primitive living speciespossess additional non-Newtonian properties which are not included in the lawsof Newtonian or statistical mechanics. These properties follow from a privilegedability of living species to possess a self-image (a concept introduced inmathematical psychology). In this paper we consider the existence of aself-image as a postulate to be added to classical physics for modeling behavior ofliving systems. We show that self-image can be incorporated into the mathematicalformalism of a nonlinear dynamics which evolves in probability space. Wedemonstrate that one of the basic invariants of living systems is their ability topredict the future, which is associated with intelligence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1003622107129
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  • 5
    Electronic Resource
    Electronic Resource
    The problem of irreversibility in Newtonian dynamics (1992)
    Springer
    International journal of theoretical physics 31 (1992), S. 333-342 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new type of dissipation function which does not satisfy the Lipschitz condition at equilibrium states is proposed. It is shown that Newtonian dynamics supplemented by this dissipation function becomes irreversible, i.e., it is not invariant with respect to time inversion. Some effects associated with the approaching of equilibria in infinite time are eliminated. New meanings of chaos and turbulence are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00673265
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  • 6
    Electronic Resource
    Electronic Resource
    Irreversibility in thermodynamics (1996)
    Springer
    International journal of theoretical physics 35 (1996), S. 347-382 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The problem of irreversibility in thermodynamics is revisited and analyzed on the microscopic, stochastic, and macroscopic levels of description. It is demonstrated that Newtonian dynamics can be represented in the Reynolds form when each dynamical variable is decomposed into mean and fluctuation components. Additional equations coupling fluctuations and the mean values follow from the stabilization principle. The main idea of this principle is that the fluctuations must be selected from the condition that they suppress the original instability down to a neutral stability. Supplemented by the stabilization principle, the Hamiltonian or Lagrangian formalisms can describe the transition from fully reversible to irreversible motions as a result of the decomposition of chaotic motions (which are very likely to occur in many-body problems) into regular (macroscopic) motions and fluctuations. On the stochastic level of description, a new phenomenological force with non-Lipschitz properties is introduced. This force, as a resultant of a large number of collisions of a selected particle with other particles, has characteristics which are uniquely defined by the thermodynamic parameters of the process under consideration, and it represents a part of the mathematical formalism describing a random-walk-like process without invoking any probabilistic arguments. Additional non-Lipschitz thermodynamic forces are incorporated into macroscopic models of transport phenomena in order to introduce a time scale. These forces are effective only within a small domain around equilibria. Without causing any changes in other domains, they are responsible for the finite time of approaching equilibria. Such a property is very important for the interpretation of irreversibility on the macroscopic scale.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02083821
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  • 7
    Electronic Resource
    Electronic Resource
    Quantum Neural Nets (1998)
    Springer
    International journal of theoretical physics 37 (1998), S. 651-684 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The capacity of classical neurocomputers islimited by the number of classical degrees of freedom,which is roughly proportional to the size of thecomputer. By contrast, a hypothetical quantumneurocomputer can implement an exponentially larger number ofthe degrees of freedom within the same size. In thispaper an attempt is made to reconcile the linearreversible structure of quantum evolution with nonlinear irreversible dynamics for neuralnets.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026656110699
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  • 8
    Electronic Resource
    Electronic Resource
    Physical models of cognition (1994)
    Springer
    International journal of theoretical physics 33 (1994), S. 1113-1161 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper presents and discusses physical models for simulating some aspects of neural intelligence, and, in particular, the process of cognition. The main departure from the classical approach here is in utilization of a terminal version of classical dynamics introduced by the author earlier. Based upon violations of the Lipschitz condition at equilibrium points, terminal dynamics attains two new fundamental properties: it is spontaneous and nondeterministic. Special attention is focused on terminal neurodynamics as a particular architecture of terminal dynamics which is suitable for modeling of information flows. Terminal neurodynamics possesses a well-organized probabilistic structure which can be analytically predicted, prescribed, and controlled, and therefore which presents a powerful tool for modeling real-life uncertainties. Two basic phenomena associated with random behavior of neurodynamic solutions are exploited. The first one is a stochastic attractor—a stable stationary stochastic process to which random solutions of a closed system converge. As a model of the cognition process, a stochastic attractor can be viewed as a universal tool for generalization and formation of classes of patterns. The concept of stochastic attractor is applied to model a collective brain paradigm explaining coordination between simple units of intelligence which perform a collective task without direct exchange of information. The second fundamental phenomenon discussed is terminal chaos which occurs in open systems. Applications of terminal chaos to information fusion as well as to explanation and modeling of coordination among neurons in biological systems are discussed. It should be emphasized that all the models of terminal neurodynamics are implementable in analog devices, which means that all the cognition processes discussed in the paper are reducible to the laws of Newtonian mechanics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01882756
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  • 9
    Electronic Resource
    Electronic Resource
    Postinstability models in dynamics (1994)
    Springer
    International journal of theoretical physics 33 (1994), S. 2215-2280 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper is devoted to the concept of instability in dynamical systems with the main emphasis on orbital, Hadamard, and Reynolds instabilities. It demonstrates that the requirement about differentiability in dynamics in some cases is not consistent with the physical nature of motions, and may lead to unrealistic solutions. Special attention is paid to the fact that instability is not an invariant of motion: it depends upon frames of reference, the metric of configuration space, and classes of functions selected for mathematical models of physical phenomena. This leads to the possibility of elimination of certain types of instabilities (in particular, those which lead to chaos and turbulence) by enlarging the class of functions using the Reynolds-type transformation in combination with the stabilization principle: the additional terms (the so-called Reynolds stresses) are found from the conditions that they suppress the original instability. Based upon these ideas, a new approach to chaos and turbulence as well as a new mathematical formalism for nonlinear dynamics are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00675803
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  • 10
    Electronic Resource
    Electronic Resource
    Terminal model of Newtonian dynamics (1993)
    Springer
    International journal of theoretical physics 32 (1993), S. 159-190 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new type of dissipation function which does not satisfy the Lipschitz condition at equilibrium states is proposed. Newtonian dynamics supplemented by this dissipation function becomes irreversible and has a well-organized probabilistic structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00674403
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