The Experts below are selected from a list of 15939 Experts worldwide ranked by ideXlab platform
Marius E. Yamakou - One of the best experts on this subject based on the ideXlab platform.
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Chaotic synchronization of memristive neurons: Lyapunov Function versus Hamilton Function
Nonlinear Dynamics, 2020Co-Authors: Marius E. YamakouAbstract:In this paper, we consider a 5-dimensional Hindmarsh–Rose neuron model. This improved version of the original model shows rich dynamical behaviors, including a chaotic super-bursting regime. This regime promises a greater information encoding capacity than the standard bursting activity. Based on the Krasovskii–Lyapunov stability theory, the sufficient conditions (on the synaptic strengths and magnetic gain parameters) for stable chaotic synchronization of the model are obtained. Based on Helmholtz’s theorem, the Hamilton Function of the corresponding error dynamical system is also obtained. It is shown that the time variation of this Hamilton Function along trajectories can play the role of the time variation of the Lyapunov Function—in determining the stability of the synchronization manifold. Numerical computations indicate that as the synaptic strengths and the magnetic gain parameters change, the time variation of the Hamilton Function is always nonzero (i.e., a relatively large positive or negative value) only when the time variation of the Lyapunov Function is positive, and zero (or vanishingly small) only when the time variation of the Lyapunov Function is also zero. This, therefore, paves an alternative way to determine the stability of synchronization manifolds and can be particularly useful for systems whose Lyapunov Function is difficult to construct, but whose Hamilton Function corresponding to the dynamic error system is easier to calculate.
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Chaotic Synchronization of memristive neurons: Lyapunov Function versus Hamilton Function.
arXiv: Adaptation and Self-Organizing Systems, 2020Co-Authors: Marius E. YamakouAbstract:We study the dynamical behaviors of this improved memristive neuron model by changing external harmonic current and the magnetic gain parameters. The model shows rich dynamics including periodic and chaotic spiking and bursting, and remarkably, chaotic super-bursting, which has greater information encoding potentials than a standard bursting activity. Based on Krasovskii-Lyapunov stability theory, the sufficient conditions (on the synaptic strengths and magnetic gain parameters) for the chaotic synchronization of the improved model are obtained. Based on Helmholtz's theorem, the Hamilton Function of the corresponding error dynamical system is also obtained. It is shown that the time variation of this Hamilton Function along trajectories can play the role of the time variation of the Lyapunov Function - in determining the asymptotic stability of the synchronization manifold. Numerical computations indicate that as the synaptic strengths and the magnetic gain parameters change, the time variation of the Hamilton Function is always non-zero (i.e., a relatively large positive or negative value) only when the time variation of the Lyapunov Function is positive, and zero (or vanishingly small) only when the time variation of the Lyapunov Function is also zero. This clearly therefore paves an alternative way to determine the asymptotic stability of synchronization manifolds, and can be particularly useful for systems whose Lyapunov Function is difficult to construct, but whose Hamilton Function corresponding to the dynamic error system is easier to calculate.
Piotr Jaranowski - One of the best experts on this subject based on the ideXlab platform.
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Erratum: Third post-Newtonian higher order ADM Hamilton dynamics for two-body point-mass systems [Phys. Rev. D 57, 7274 (1998)]
Physical Review D, 2000Co-Authors: Piotr Jaranowski, Gerhard SchäferAbstract:The paper presents the conservative dynamics of two-body point-mass systems up to the third post-Newtonian order ($1/c^6$). The two-body dynamics is given in terms of a higher order ADM Hamilton Function which results from a third post-Newtonian Routh Functional for the total field-plus-matter system. The applied regularization procedures, together with making use of distributional differentiation of homogeneous Functions, give unique results for the terms in the Hamilton Function apart from the coefficient of the term $(\nu p_{i}{\pa_{i}})^2r^{-1}$. The result suggests an invalidation of the binary point-mass model at the third post-Newtonian order.Comment: LaTeX, 27 pages, submitted to Physical Review
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Third post-Newtonian higher order ADM Hamilton dynamics for two-body point-mass systems
Physical Review D, 1998Co-Authors: Piotr Jaranowski, Gerhard SchaeferAbstract:The paper presents the conservative dynamics of two-body point-mass systems up to the third post-Newtonian order ($1/c^6$). The two-body dynamics is given in terms of a higher order ADM Hamilton Function which results from a third post-Newtonian Routh Functional for the total field-plus-matter system. The applied regularization procedures, together with making use of distributional differentiation of homogeneous Functions, give unique results for the terms in the Hamilton Function apart from the coefficient of the term $(\nu p_{i}{\pa_{i}})^2r^{-1}$. The result suggests an invalidation of the binary point-mass model at the third post-Newtonian order.
Gerhard Schaefer - One of the best experts on this subject based on the ideXlab platform.
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Third post-Newtonian higher order ADM Hamilton dynamics for two-body point-mass systems
Physical Review D, 1998Co-Authors: Piotr Jaranowski, Gerhard SchaeferAbstract:The paper presents the conservative dynamics of two-body point-mass systems up to the third post-Newtonian order ($1/c^6$). The two-body dynamics is given in terms of a higher order ADM Hamilton Function which results from a third post-Newtonian Routh Functional for the total field-plus-matter system. The applied regularization procedures, together with making use of distributional differentiation of homogeneous Functions, give unique results for the terms in the Hamilton Function apart from the coefficient of the term $(\nu p_{i}{\pa_{i}})^2r^{-1}$. The result suggests an invalidation of the binary point-mass model at the third post-Newtonian order.
Gerhard Schäfer - One of the best experts on this subject based on the ideXlab platform.
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Erratum: Third post-Newtonian higher order ADM Hamilton dynamics for two-body point-mass systems [Phys. Rev. D 57, 7274 (1998)]
Physical Review D, 2000Co-Authors: Piotr Jaranowski, Gerhard SchäferAbstract:The paper presents the conservative dynamics of two-body point-mass systems up to the third post-Newtonian order ($1/c^6$). The two-body dynamics is given in terms of a higher order ADM Hamilton Function which results from a third post-Newtonian Routh Functional for the total field-plus-matter system. The applied regularization procedures, together with making use of distributional differentiation of homogeneous Functions, give unique results for the terms in the Hamilton Function apart from the coefficient of the term $(\nu p_{i}{\pa_{i}})^2r^{-1}$. The result suggests an invalidation of the binary point-mass model at the third post-Newtonian order.Comment: LaTeX, 27 pages, submitted to Physical Review
S.v. Petrov - One of the best experts on this subject based on the ideXlab platform.
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The nature of bifurcations in the rotational dynamics of H2X triatomic molecules
Russian Journal of Physical Chemistry A, 2004Co-Authors: S.v. Petrov, A. P. PyshchevAbstract:Bifurcations in the rotational dynamics of H 2 X molecules are shown to be caused by a combination of potential parameters and masses of nuclei rather than symmetry. The use of a rigid deformation model with a specially adjusted potential allows an analytic equation to he obtained for the rotational Hamilton Function and the critical angular momentum value as a Function of molecular parameters.
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Molecular rotation based on the minimization of the ro-vibrational Hamilton Function
12th Symposium and School on High-Resolution Molecular Spectroscopy, 1997Co-Authors: S.v. PetrovAbstract:Our method of attack of the molecular rotation in the case when the ro-vib interaction can not be considered as a small one involves three steps. Firstly, so called effective classical energy of the molecular rotation is defined as the minimum of the exact classical ro-vib Hamilton Function (it is suggested that the dependence of Hamilton Function on the angular momentum components is the parametric one). The second step consists in the qualitative analysis of the classical rotational energy Function using well known conception of the rotational energy surface (RES). The non- local bifurcation in rotational dynamics of isotopically substituted P 4 molecule is considered as an example. The third step consists in the construction of an effective quantum rotational Hamiltonian from the classical rotational energy Function. As an example, the rotational levels of KCN molecule in the ground vibrational state are calculated.
