Commentary to “pharmacokinetics from a dynamical systems point of view”

1989 ◽  
Vol 17 (3) ◽  
pp. 393-397 ◽  
Author(s):  
Michael Weiss
Keyword(s):  
Dynamical Systems ◽  
Point Of View

scholarly journals On some kinds of dense orbits in general nonautonomous dynamical systems

2020 ◽  
Vol 7 (1) ◽  
pp. 163-175
Author(s):  
Mehdi Pourbarat
Keyword(s):  
Dynamical Systems ◽  
Initial Conditions ◽  
Point Of View ◽  
Topological Conjugacy ◽  
Topological Transitivity ◽  
Nonautonomous Systems ◽  
Nonautonomous Dynamical Systems ◽  
Sensitive Dependence ◽  
Dense Orbits

AbstractWe study the theory of universality for the nonautonomous dynamical systems from topological point of view related to hypercyclicity. The conditions are provided in a way that Birkhoff transitivity theorem can be extended. In the context of generalized linear nonautonomous systems, we show that either one of the topological transitivity or hypercyclicity give sensitive dependence on initial conditions. Meanwhile, some examples are presented for topological transitivity, hypercyclicity and topological conjugacy.

SURVEY Towards a global view of dynamical systems, for the C1-topology

2011 ◽  
Vol 31 (4) ◽  
pp. 959-993 ◽  
Author(s):  
C. BONATTI
Keyword(s):  
Dynamical Systems ◽  
Compact Manifold ◽  
Global Structure ◽  
Point Of View ◽  
List Type ◽  
Global View ◽  
Local Phenomenon ◽  
Generic Dynamics

AbstractThis paper suggests a program for getting a global view of the dynamics of diffeomorphisms, from the point of view of the C1-topology. More precisely, given any compact manifold M, one splits Diff1(M) into disjoint C1-open regions whose union is C1-dense, and conjectures state that each of these open sets and their complements is characterized by the presence of: •either a robust local phenomenon;•or a global structure forbidding this local phenomenon. Other conjectures state that some of these regions are empty. This set of conjectures draws a global view of the dynamics, putting in evidence the coherence of the numerous recent results on C1-generic dynamics.

scholarly journals Coherent structures and chaotic advection in three dimensions

2010 ◽  
Vol 654 ◽  
pp. 1-4 ◽  
Author(s):  
STEPHEN WIGGINS
Keyword(s):  
Dynamical Systems ◽  
Fluid Mechanics ◽  
Coherent Structures ◽  
Three Dimensional ◽  
Point Of View ◽  
Three Dimensions ◽  
Chaotic Advection ◽  
Periodic Flow ◽  
Two Dimensional ◽  
Time Periodic

In the 1980s the incorporation of ideas from dynamical systems theory into theoretical fluid mechanics, reinforced by elegant experiments, fundamentally changed the way in which we view and analyse Lagrangian transport. The majority of work along these lines was restricted to two-dimensional flows and the generalization of the dynamical systems point of view to fully three-dimensional flows has seen less progress. This situation may now change with the work of Pouransari et al. (J. Fluid Mech., this issue, vol. 654, 2010, pp. 5–34) who study transport in a three-dimensional time-periodic flow and show that completely new types of dynamical systems structures and consequently, coherent structures, form a geometrical template governing transport.

NUMERICAL METHODS FOR FUZZY INITIAL VALUE PROBLEMS

1999 ◽  
Vol 07 (05) ◽  
pp. 439-461 ◽  
Author(s):  
EYKE HÜLLERMEIER
Keyword(s):  
Dynamical Systems ◽  
Numerical Methods ◽  
Fuzzy Set ◽  
Initial Value Problems ◽  
Point Of View ◽  
Reachable Sets ◽  
Large Set ◽  
Initial Value ◽  
System States ◽  
Probabilistic Point

In this paper, fuzzy initial value problems for modelling aspects of uncertainty in dynamical systems are introduced and interpreted from a probabilistic point of view. Due to the uncertainty incorporated in the model, the behavior of dynamical systems modelled in this way will generally not be unique. Rather, we obtain a large set of trajectories which are more or less compatible with the description of the system. We propose so-called fuzzy reachable sets for characterizing the (fuzzy) set of solutions to a fuzzy initial value problem. Loosely spoken, a fuzzy reachable set is defined as the (fuzzy) set of possible system states at a certain point of time, with given constraints concerning the initial system state and the system evolution. The main-part of the paper is devoted to the development of the numerical methods for the approximation of such sets. Algorithms for precise as well as outer approximations are presented. It is shown that fuzzy reachable sets can be approximated to any degree of accuracy under certain assumptions. Our method is illustrated by means of an example from the field of economics.

scholarly journals Dynamics and spectral theory of quasi-periodic Schrödinger-type operators

2016 ◽  
Vol 37 (8) ◽  
pp. 2353-2393 ◽  
Author(s):  
C. A. MARX ◽  
S. JITOMIRSKAYA
Keyword(s):  
Dynamical Systems ◽  
Spectral Theory ◽  
Point Of View ◽  
Schrödinger Type Operators

We survey the theory of quasi-periodic Schrödinger-type operators, focusing on the advances made since the early 2000s by adopting a dynamical systems point of view.

Stability of Dynamical Systems With Multiple Nonlinearities

1987 ◽  
Vol 109 (4) ◽  
pp. 410-413 ◽  
Author(s):  
Norio Miyagi ◽  
Hayao Miyagi
Keyword(s):  
Dynamical System ◽  
Stability Analysis ◽  
Dynamical Systems ◽  
Lyapunov Function ◽  
Stability Region ◽  
Direct Method ◽  
Essential Feature ◽  
Point Of View ◽  
Stability Of Dynamical Systems ◽  
The Stability

This note applies the direct method of Lyapunov to stability analysis of a dynamical system with multiple nonlinearities. The essential feature of the Lyapunov function used in this note is a non-Lure´ type Lyapunov function which surpasses the Lure´-type Lyapunov function from the point of view of the stability region guaranteed. A modified version of the multivariable Popov criterion is used to construct non-Lure´ type Lyapunov function, which allow for the dynamical sytems with multiple nonlinearities.

scholarly journals Peakon, Solitary and Smooth Periodic Wave Solutions for a Modification of theK(2,2)Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Qing Meng ◽  
Bin He
Keyword(s):  
Dynamical Systems ◽  
Solitary Wave ◽  
Periodic Wave ◽  
Point Of View ◽  
Phase Portraits ◽  
Periodic Waves ◽  
Solitary Wave Solutions ◽  
Bifurcation Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions

We consider a modification of theK(2,2)equationut=2uuxxx+2kuxuxx+2uuxusing the bifurcation method of dynamical systems and the method of phase portraits analysis. From dynamic point of view, some peakons, solitary, and smooth periodic waves are found and their exact parametric representations are presented. Also, the coexistence of peakon and solitary wave solutions is investigated.

About A. N. Kolmogorov's work on the entropy of dynamical systems

1988 ◽  
Vol 8 (4) ◽  
pp. 501-502 ◽  
Author(s):  
Ya. G. Sinai
Keyword(s):  
Dynamical Systems ◽  
Unitary Operator ◽  
Point Spectrum ◽  
Point Of View ◽  
Stochastic Integrals ◽  
State University ◽  
Multiple Stochastic Integrals ◽  
Lebesgue Spectrum ◽  
Probabilistic Point ◽  
Moscow State University

In the fall of 1957 A. N. Kolmogorov started lecturing on the theory of dynamical systems and supervised a seminar on the same theme at the Mechanical–Mathematical Department of Moscow State University. He began his lectures with the theory of systems with a pure point spectrum, which he approached from a probabilistic point of view. This approach, undoubtedly, has many advantages. In the seminar we studied Ito's theory of multiple stochastic integrals and, under the supervision of A. N. Kolmogorov, I. V. Girsanov constructed an example of a Gaussian dynamical system with a simple continuous spectrum. At one of the meetings of the seminar, still before the advent of entropy, Kolmogorov suggested a proof of an assertion, which today would read: the unitary operator induced by a K-automorphism has a countable Lebesgue spectrum. At this point Kolmogorov was studying Shannon's theory of information and the concept of the capacity of functional spaces. Judging by his well known article, we can say that the first of these, and all that is related to it, played a big role in the development of information theory in our country. The investigation of capacity is connected with Kolmogorov's work on Hilbert's 13th problem and was summarized in his well-known survey co-authored by V. M. Tihomirov.

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