scholarly journals A cyclic system with delay and its characteristic equation

2020 ◽  
Vol 13 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Elena Braverman ◽  
◽  
Karel Hasik ◽  
Anatoli F. Ivanov ◽  
Sergei I. Trofimchuk ◽  
...  
Keyword(s):  
Characteristic Equation ◽  
Cyclic System ◽  
System With Delay

Investigating Dynamics of One Weakly Nonlinear System with Delay Argument

2018 ◽  
Vol 50 (1) ◽  
pp. 20-38 ◽  
Author(s):  
Denis Ya. Khusainov ◽  
Jozef Diblik ◽  
Jaromir Bashtinec ◽  
Andrey V. Shatyrko
Keyword(s):  
Nonlinear System ◽  
Weakly Nonlinear ◽  
Delay Argument ◽  
System With Delay ◽  
Weakly Nonlinear System

scholarly journals Complete Controllability Conditions for Linear Singularly Perturbed Time-Invariant Systems with Multiple Delays via Chang-Type Transformation

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 71 ◽  
Author(s):  
Olga Tsekhan
Keyword(s):  
Sufficient Conditions ◽  
Singularly Perturbed ◽  
Degenerate System ◽  
Multiple Delays ◽  
Complete Controllability ◽  
Singularly Perturbed System ◽  
System With Delay ◽  
Perturbed System ◽  
Time Invariant ◽  
Controllability Conditions

The problem of complete controllability of a linear time-invariant singularly-perturbed system with multiple commensurate non-small delays in the slow state variables is considered. An approach to the time-scale separation of the original singularly-perturbed system by means of Chang-type non-degenerate transformation, generalized for the system with delay, is used. Sufficient conditions for complete controllability of the singularly-perturbed system with delay are obtained. The conditions do not depend on a singularity parameter and are valid for all its sufficiently small values. The conditions have a parametric rank form and are expressed in terms of the controllability conditions of two systems of a lower dimension than the original one: the degenerate system and the boundary layer system.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

scholarly journals A Biologically Active Insulin Analog with an Enlarged Intrachain Cyclic System

1973 ◽  
Vol 248 (21) ◽  
pp. 7304-7309
Author(s):  
Alexandros Cosmatos ◽  
Panayotis G. Katsoyannis
Keyword(s):  
Biologically Active ◽  
Insulin Analog ◽  
Cyclic System

scholarly journals Testing Stability of Digital Filters Using Optimization Methods with Phase Analysis

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1488
Author(s):  
Damian Trofimowicz ◽  
Tomasz P. Stefański
Keyword(s):  
Unit Circle ◽  
Phase Analysis ◽  
Characteristic Equation ◽  
Digital Filter ◽  
Digital Filters ◽  
Computing Time ◽  
Complex Function ◽  
Stochastic Methods ◽  
Final Population ◽  
Candidate Regions

In this paper, novel methods for the evaluation of digital-filter stability are investigated. The methods are based on phase analysis of a complex function in the characteristic equation of a digital filter. It allows for evaluating stability when a characteristic equation is not based on a polynomial. The operation of these methods relies on sampling the unit circle on the complex plane and extracting the phase quadrant of a function value for each sample. By calculating function-phase quadrants, regions in the immediate vicinity of unstable roots (i.e., zeros), called candidate regions, are determined. In these regions, both real and imaginary parts of complex-function values change signs. Then, the candidate regions are explored. When the sizes of the candidate regions are reduced below an assumed accuracy, then filter instability is verified with the use of discrete Cauchy’s argument principle. Three different algorithms of the unit-circle sampling are benchmarked, i.e., global complex roots and poles finding (GRPF) algorithm, multimodal genetic algorithm with phase analysis (MGA-WPA), and multimodal particle swarm optimization with phase analysis (MPSO-WPA). The algorithms are compared in four benchmarks for integer- and fractional-order digital filters and systems. Each algorithm demonstrates slightly different properties. GRPF is very fast and efficient; however, it requires an initial number of nodes large enough to detect all the roots. MPSO-WPA prevents missing roots due to the usage of stochastic space exploration by subsequent swarms. MGA-WPA converges very effectively by generating a small number of individuals and by limiting the final population size. The conducted research leads to the conclusion that stochastic methods such as MGA-WPA and MPSO-WPA are more likely to detect system instability, especially when they are run multiple times. If the computing time is not vitally important for a user, MPSO-WPA is the right choice, because it significantly prevents missing roots.

Characteristic equation of a matrix

1970 ◽  
Vol 5 (3) ◽  
pp. 31-31
Author(s):  
T. A. Bickart
Keyword(s):  
Characteristic Equation
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