Study of Dynamic Modes of Current Stabilization Systems of Powerful Electromagnets with Pulse-Width Modulation

2021 ◽  
Vol 22 (6) ◽  
pp. 313-320
Author(s):  
M. S. Lur’e ◽  
O. M. Lur’e ◽  
A. S. Frolov
Keyword(s):  
Pulse Width ◽  
Pulse Width Modulation ◽  
Functional Differential Equations ◽  
Original System ◽  
Nyquist Stability ◽  
Detailed Assessment ◽  
Functional Differential ◽  
The Stability ◽  
Automatic Systems ◽  
A Current

This study is devoted to the consideration of a method for assessing the stability of systems with pulse-width modulation, based on the linearization of its equivalent system with pulse-width modulation. An approximate study of the dynamic modes of operation of systems with pulse-width modulation, taking into account the stability for the system of automatic control of the supply current of electromagnets under the conditions of external and internal interference, is carried out. Variants of execution of schemes of pulse-width regulators for the power supply of an electromagnet based on a unipolar and bipolar element with pulse-width modulation are presented. The possibility of linearization of systems with pulse-width modulation for the subsequent detailed assessment of the stability of such systems is shown. The prospects of using functional differential equations for stability analysis of automatic systems with pulse-width modulation are shown. The frequency characteristics of an equivalent pulse system are analyzed using the example of a current stabilization system of high-power electromagnets with a pulse-width regulator, taking into account the replacement of the latitude modulation by the amplitude one. Based on the analysis of the resulting transfer function, which is a stable linearized equivalent open system, the ways of evaluating the stability of the original system with pulse-width modulation using the Nyquist stability criterion are proposed. The conclusion is made about the advantage of a system with PWM, in relation to a system with AIM, in terms of stability, and recommendations are given for the use of the obtained data in the analysis oftransients in such systems.

scholarly journals Bifurcation Analysis in a Diffusive Mussel-Algae Model with Delay

2019 ◽  
Vol 29 (11) ◽  
pp. 1950144 ◽  
Author(s):  
Zuolin Shen ◽  
Junjie Wei
Keyword(s):  
Hopf Bifurcation ◽  
Functional Differential Equations ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Delayed Reaction ◽  
Center Manifold Reduction ◽  
Existence Of Positive Solutions ◽  
Boundary Equilibrium ◽  
Functional Differential ◽  
The Stability

In this paper, we consider the dynamics of a delayed reaction–diffusion mussel-algae system subject to Neumann boundary conditions. When the delay is zero, we show the existence of positive solutions and the global stability of the boundary equilibrium. When the delay is not zero, we obtain the stability of the positive constant steady state and the existence of Hopf bifurcation by analyzing the distribution of characteristic values. By using the theory of normal form and center manifold reduction for partial functional differential equations, we derive an algorithm that determines the direction of Hopf bifurcation and the stability of bifurcating periodic solutions. Finally, some numerical simulations are carried out to support our theoretical results.

On the stability of invariant sets of functional differential equations

2003 ◽  
Vol 55 (6) ◽  
pp. 641-656 ◽  
Author(s):  
Stephen R. Bernfeld ◽  
Constantin Corduneanu ◽  
Alexander O. Ignatyev
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Invariant Sets ◽  
Functional Differential ◽  
The Stability

scholarly journals Implicit difference schemes for quasilinear parabolic functional equations

2012 ◽  
Vol 45 (4) ◽  
Author(s):  
Milena Matusik
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Initial Boundary ◽  
Difference Schemes ◽  
New Class ◽  
Implicit Difference Schemes ◽  
Functional Differential ◽  
The Stability ◽  
Quasilinear Parabolic

AbstractWe present a new class of numerical methods for quasilinear parabolic functional differential equations with initial boundary conditions of the Robin type. The numerical methods are difference schemes which are implicit with respect to time variable. We give a complete convergence analysis for the methods and we show that the new methods are considerable better than the explicit schemes. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for given functions with respect to functional variables. Results obtained in the paper can be applied to differential equations with deviated variables and to differential integral problems.

scholarly journals Ultimate Boundedness of the Systems Governed by Stochastic Differential Equations

1972 ◽  
Vol 47 ◽  
pp. 111-144 ◽  
Author(s):  
Yoshio Miyahara
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stochastic Differential Equations ◽  
Functional Differential Equations ◽  
Ultimate Boundedness ◽  
Functional Differential ◽  
The Stability

The stability of the systems given by ordinary differential equations or functional-differential equations has been studied by many mathematicians. The most powerful tool in this field seems to be the Liapunov’s second method (see, for example [6]).

STABILITY ANALYSIS FOR DELAYED CELLULAR NEURAL NETWORKS BASED ON LINEAR MATRIX INEQUALITY APPROACH

2004 ◽  
Vol 14 (09) ◽  
pp. 3377-3384 ◽  
Author(s):  
XIAOFENG LIAO ◽  
KWOK-WO WONG ◽  
SHIZHONG YANG
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Linear Matrix Inequality Approach ◽  
Functional Differential ◽  
The Stability

Some sufficient conditions for the asymptotic stability of cellular neural networks with time delay are derived using the Lyapunov–Krasovskii stability theory for functional differential equations as well as the linear matrix inequality (LMI) approach. The analysis shows how some well-known results can be refined and generalized in a straightforward manner. Moreover, the stability criteria obtained are delay-independent. They are less conservative and restrictive than those reported so far in the literature, and provide a more general set of criteria for determining the stability of delayed cellular neural networks.

scholarly journals Stability and bifurcation in a ratio-dependent Holling-III system with diffusion and delay

2014 ◽  
Vol 19 (1) ◽  
pp. 132-153 ◽  
Author(s):  
Wenjie Zuo ◽  
Junjie Wei
Keyword(s):  
Functional Response ◽  
Functional Differential Equations ◽  
Hopf Bifurcations ◽  
Normal Form Theory ◽  
Center Manifold Reduction ◽  
The Maximum Principle ◽  
Boundary Equilibrium ◽  
Ratio Dependent ◽  
Functional Differential ◽  
The Stability

A diffusive ratio-dependent predator-prey system with Holling-III functional response and delay effects is considered. Global stability of the boundary equilibrium and the stability of the unique positive steady state and the existence of spatially homogeneous and inhomogeneous periodic solutions are investigated in detail, by the maximum principle and the characteristic equations. Ratio-dependent functional response exhibits rich spatiotemporal patterns. It is found that, the system without delay is dissipative and uniformly permanent under certain conditions, the delay can destabilize the positive constant equilibrium and spatial Hopf bifurcations occur as the delay crosses through some critical values. Then, the direction and the stability of Hopf bifurcations are determined by applying the center manifold reduction and the normal form theory for partial functional differential equations. Some numerical simulations are carried out to illustrate the theoretical results.

INVESTIGATION OF THE IMPACT OF DELAY IN ONE MATHEMATICAL MODEL OF WORLD DEVELOPMENT DYNAMICS

2021 ◽  
Vol 6 ◽  
pp. 47-54
Author(s):  
Denis Khusainov ◽  
◽  
Andrey Shatyrko ◽  
Alexey Bychkov ◽  
Bedrick Puza ◽  
...  
Keyword(s):  
Differential Equations ◽  
Time Lag ◽  
Functional Differential Equations ◽  
Deviating Arguments ◽  
System Equilibrium ◽  
Constant Coefficients ◽  
Functional Differential ◽  
The Stability ◽  
The Impact ◽  
World Development

There is a large number of works devoted to the dynamics of world development. But very few of them have clear abstract mathematical models of the corresponding processes. This work is devoted to further deepening and mathematical abstraction of the study of world development process. The qualitative analysis of linear and modified nonlinear model in the form of systems of inhomogeneous differential equations is carried out. Their steady states are calculated, explicit analytical solutions are presented. For the first time, a model taking into account the time delay factor is proposed, which is written in the form of functional-differential equations with argument deviation. It is shown that with such an introduction to the model of a delayed argument, the system can be reduced to a system of linear inhomogeneous differential equations with constant coefficients without delay, and the stability of the steady state of the system equilibrium under study will be affected only by linear terms of equations without argument deviation. This fact well correlates with the socio-economic interpretation of this problem. In the future, the work will focus on studying the influence of not one but several factors of time lag, when the model is presented as a system of functional-differential equations with several different deviating arguments in equations responsible for the dynamics of a particular process dynamics of world development.

Sign in / Sign up

Export Citation Format

Share Document