The Lyapunov characteristic exponents-applications to celestial mechanics

1984 ◽  
Vol 34 (1-4) ◽  
pp. 95-115 ◽  
Author(s):  
Cl. Froeschl�
Keyword(s):  
Celestial Mechanics ◽  
Characteristic Exponents ◽  
Lyapunov Characteristic Exponents

scholarly journals Distributed Control and the Lyapunov Characteristic Exponents in the Model of Infectious Diseases

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
M. Bershadsky ◽  
M. Chirkov ◽  
A. Domoshnitsky ◽  
S. Rusakov ◽  
I. Volinsky
Keyword(s):  
Infectious Diseases ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Distributed Control ◽  
Stationary Point ◽  
Treatment Time ◽  
Simulation Models ◽  
Characteristic Exponents ◽  
Data Comparison ◽  
Lyapunov Characteristic Exponents

The Marchuk model of infectious diseases is considered. Distributed control to make convergence to stationary point faster is proposed. Medically, this means that treatment time can be essentially reduced. Decreasing the concentration of antigen, this control facilitates the patient’s condition and gives a certain new idea of treating the disease. Our approach involves the analysis of integro-differential equations. The idea of reducing the system of integro-differential equations to a system of ordinary differential equations is used. The final results are given in the form of simple inequalities on the parameters. The results of numerical calculations of simulation models and data comparison in the case of using distributive control and in its absence are given.

scholarly journals Deterministic chaos in pendulum systems with delay

2019 ◽  
Vol 4 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Aleksandr Shvets ◽  
Alexander Makaseyev
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Differential Equations ◽  
Deterministic Chaos ◽  
Phase Portraits ◽  
Characteristic Exponents ◽  
Systems Of Differential Equations ◽  
Lyapunov Characteristic Exponents ◽  
The Mathematical Model ◽  
Equations With Delay

AbstractDynamic system "pendulum - source of limited excitation" with taking into account the various factors of delay is considered. Mathematical model of the system is a system of ordinary differential equations with delay. Three approaches are suggested that allow to reduce the mathematical model of the system to systems of differential equations, into which various factors of delay enter as some parameters. Genesis of deterministic chaos is studied in detail. Maps of dynamic regimes, phase-portraits of attractors of systems, phase-parametric characteristics and Lyapunov characteristic exponents are constructed and analyzed. The scenarios of transition from steady-state regular regimes to chaotic ones are identified. It is shown, that in some cases the delay is the main reason of origination of chaos in the system "pendulum - source of limited excitation".

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