scholarly journals Qualitative Study of a Well-Stirred Isothermal Reaction Model

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 938
Author(s):  
Barbara Arcet ◽  
Maša Dukarić ◽  
Zhibek Kadyrsizova
Keyword(s):  
Mathematical Model ◽  
Jacobian Matrix ◽  
Temporal Evolution ◽  
Sufficient Conditions ◽  
Reaction System ◽  
Reaction Model ◽  
Dimensional System ◽  
Two Dimensional ◽  
Isothermal Reaction ◽  
Two Dimensional System

We consider a two-dimensional system which is a mathematical model for a temporal evolution of a well-stirred isothermal reaction system. We give sufficient conditions for the existence of purely imaginary eigenvalues of the Jacobian matrix of the system at its fixed points. Moreover, we show that the system admits a supercritical Hopf bifurcation.

Analysis and modeling of an inverted pendulum system

2021 ◽  
Author(s):  
Keyword(s):  
Mathematical Model ◽  
Nonlinear System ◽  
Inverted Pendulum ◽  
System Analysis ◽  
Dimensional System ◽  
Two Dimensional ◽  
System Operation ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Two Dimensional System

A nonlinear system, which consists of an inverted pendulum mounted on a cart with an electric drive, is considered. A mathematical model is created, its analysis and modeling of the investigated two-dimensional system operation is carried out. Keywords mathematical model; inverted pendulum; system analysis; state space

scholarly journals Stability and Bifurcation for a Single-Species Model with Delay Weak Kernel and Constant Rate Harvesting

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Xiangrui Li ◽  
Shuibo Huang
Keyword(s):  
Hopf Bifurcation ◽  
Sufficient Conditions ◽  
Single Species ◽  
Critical Value ◽  
Dimensional System ◽  
Two Dimensional ◽  
Constant Rate ◽  
Lyapunov Coefficient ◽  
Two Dimensional System ◽  
Single Species Model

In this paper, we consider the effect of constant rate harvesting on the dynamics of a single-species model with a delay weak kernel. By a simple transformation, the single-species model is transformed into a two-dimensional system. The existence and the stability of possible equilibria under different conditions are carried out by analysing the two-dimensional system. We show that there exists a critical harvesting value such that the population goes extinct in finite time if the constant rate harvesting u is greater than the critical value, and there exists a degenerate critical point or a saddle-node bifurcation when the constant rate harvesting u equals the critical value. When the constant rate harvesting u is less than the critical value, sufficient conditions about the existence of the Hopf bifurcation are derived by topological normal form for the Hopf bifurcation and calculating the first Lyapunov coefficient. The key results obtained in the present paper are illustrated using numerical simulations. These results indicate that it is important to select the appropriate constant rate harvesting u.

Effect of partial ordering of a two-dimensional system of scatterers on the anisotropy of its kinetic coefficients

1998 ◽  
Vol 32 (10) ◽  
pp. 1116-1118
Author(s):  
N. S. Averkiev ◽  
A. M. Monakhov ◽  
A. Yu. Shik ◽  
P. M. Koenraad
Keyword(s):  
Partial Ordering ◽  
Dimensional System ◽  
Two Dimensional ◽  
Kinetic Coefficients ◽  
Two Dimensional System

Coherent Backscattering of Light in a Quasi-Two-Dimensional System

1988 ◽  
Vol 61 (10) ◽  
pp. 1214-1217 ◽  
Author(s):  
Isaac Freund ◽  
Michael Rosenbluh ◽  
Richard Berkovits ◽  
Moshe Kaveh
Keyword(s):  
Dimensional System ◽  
Two Dimensional ◽  
Coherent Backscattering ◽  
Two Dimensional System

Use of partially porous column as second dimension in comprehensive two-dimensional system for analysis of polyphenolic antioxidants

2008 ◽  
Vol 31 (19) ◽  
pp. 3297-3308 ◽  
Author(s):  
Paola Dugo ◽  
Francesco Cacciola ◽  
Miguel Herrero ◽  
Paola Donato ◽  
Luigi Mondello
Keyword(s):  
Dimensional System ◽  
Two Dimensional ◽  
Polyphenolic Antioxidants ◽  
Two Dimensional System

Electron concentration dependent fractional quantisation in a two dimensional system

1985 ◽  
Vol 56 (2) ◽  
pp. 173-176 ◽  
Author(s):  
R.G. Clark ◽  
R.J. Nicholas ◽  
M.A. Brummell ◽  
A. Usher ◽  
S. Collocott ◽  
...  
Keyword(s):  
Electron Concentration ◽  
Dimensional System ◽  
Two Dimensional ◽  
Two Dimensional System

scholarly journals The Electrostatic Energy of a Two-Dimensional System

1959 ◽  
Vol 42 ◽  
pp. 1-2
Author(s):  
LL. G. Chambers
Keyword(s):  
Complex Variable ◽  
Complex Potential ◽  
Unit Length ◽  
Electrostatic Energy ◽  
Dimensional System ◽  
Two Dimensional ◽  
Image System ◽  
Actual System ◽  
Image Domain ◽  
Two Dimensional System

The use of the complex variable z( = x + iy) and the complex potential W(= U + iV) for two-dimensional electrostatic systems is well known and the actual system in the (x, y) plane has an image system in the (U, V) plane. It does not seem to have been noticed previously that the electrostatic energy per unit length of the actual system is simply related to the area of the image domain in the (U, V) plane.

Sign in / Sign up

Export Citation Format

Share Document