scholarly journals An Octave Package to Perform Qualitative Analysis of Nonlinear Systems Immersed in R4

2020 ◽  
Author(s):  
Eder Escobar ◽  
Richard Abramonte ◽  
Antenor Aliaga ◽  
Flabio Gutierrez
Keyword(s):  
Differential Equation ◽  
Hopf Bifurcation ◽  
Qualitative Analysis ◽  
Initial Conditions ◽  
Autonomous Systems ◽  
Electronic Circuits ◽  
Four Dimensions ◽  
System Sensitivity ◽  
Linear Differential

In this work, the AutonomousSystems4D package is presented, which allows the qualitative analysis of non-linear differential equation systems in four dimensions, as well as drawing the phase surfaces by immersing R4 in R3. The package is programmed in the computational tool Octave. As a case study applied to the new Lorenz 4D System, sensitivity was found in the initial conditions, Lyapunov exponents, Kaplan Yorke dimension, a stable and unstable critical point, limit cycle, Hopf bifurcation, and hyperattractors. The package could be adapted to perform qualitative analysis and visualize phase surfaces to autonomous systems, e.g. Sprott 4D, Rossler 4D, etc. The package can be applied to problems such as: design, analysis, implementation of electronic circuits; to message encryption.

scholarly journals Existence of limit cycles for a class of autonomous systems

1983 ◽  
Vol 28 (3) ◽  
pp. 331-337
Author(s):  
Anthony Sofo
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Autonomous Systems ◽  
Non Linear ◽  
Stable Periodic ◽  
Linear Differential ◽  
Image Position

A proof is given for the existence of at least one stable periodic limit cycle solution for the polynomial non-linear differential equation of the formin some cases where the Levinson-Smith criteria are not directly applicable.

Methods for using an integro-differential equation as a model of tree height growth

1987 ◽  
Vol 17 (5) ◽  
pp. 353-356 ◽  
Author(s):  
David Hamlin ◽  
Rolfe Leary
Keyword(s):  
Differential Equation ◽  
Initial Conditions ◽  
Tree Height ◽  
Analysis Data ◽  
Equation Model ◽  
Height Growth ◽  
Integro Differential Equation ◽  
Biological Interpretation ◽  
Linear Differential ◽  
Tree Height Growth

An integro-differential equation model of tree height growth is developed, together with a biological interpretation of its coefficients. The integro-differential equation is reduced to a second order linear differential equation with constraints on its initial conditions. Because of the constraints, fitting of the differential equation is best accomplished using a multipoint boundary value approach. An example using stem analysis data is presented. The model fit the data well and was montonically increasing with an upper asymptote, although several other curve forms are possible.

Adiabatic One-Dimensional Flow of a Perfect Gas through a Rotating Tube of Uniform Cross Section

1954 ◽  
Vol 4 (4) ◽  
pp. 373-399 ◽  
Author(s):  
K. Kestin ◽  
S. K. Zaremba
Keyword(s):  
Differential Equation ◽  
Gas Turbines ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Velocity Variation ◽  
Perfect Gas ◽  
Cross Sectional ◽  
One Dimensional ◽  
Linear Differential ◽  
Entrance Velocity

SummaryThe paper contains an analysis of the flow of a perfect gas with constant specific heats through a rotating channel of constant cross-sectional area, as used in certain helicopter propulsion systems and wind-driven gas turbines. The analysis is restricted to the adiabatic one-dimensional treatment, the Coriolis accelerations acting across a section being disregarded.The equations of motion and energy are deduced and, together with the equation of continuity, reduced to an ordinary non-linear differential equation of the first order, involving a dimensionless form of velocity and distance.The patterns of the integral curves of the differential equation are discussed and sketched by examining their asymptotic behaviour as well as that in the neighbourhood of singular points. It is shown that there exists a critical value of the angular velocity below which the flow remains subsonic in the pipe, if the entrance velocity is subsonic; it may, however, become sonic at the exit of the pipe. For supercritical angular velocities the flow may become sonic or supersonic in the pipe if the entrance velocity attains a given “ correct” but subsonic value. A method of examining for the possibility of shock formation is indicated.The initial conditions for the differential equation are deduced for the design and for the performance problem, two new flow functions being introduced and tabulated to facilitate practical calculations. Formulae are also deduced for the calculation of the pressure and Mach number variation from the previously calculated velocity variation along the pipe.Finally an approximate solution in closed terms is given for the case of small entrance velocities.

Structural framework of integration and the basic law of the non-relativistic dynamics

10.12737/4044 ◽  
2014 ◽  
Vol 6 (4) ◽  
pp. 37-40
Author(s):  
Котов ◽  
P. Kotov
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Initial Conditions ◽  
Second Law ◽  
Relativistic Dynamics ◽  
Structural Framework ◽  
Finite Dimensional ◽  
Basic Law ◽  
Linear Differential

Considered finite-dimensional linear differential equation with measurable initial conditions, which describes how the second law of dynamics and offers a constructive basis of real integration of differential equations of the basic law of dynamics.

scholarly journals The study of heat transfer phenomena by using modified homotopy perturbation method coupled by Laplace transform

2020 ◽  
Vol 24 (2 Part B) ◽  
pp. 1105-1115
Author(s):  
Uriel Filobello-Nino ◽  
Hector Vazquez-Leal ◽  
Agustin Herrera-May ◽  
Roberto Ambrosio-Lazaro ◽  
Victor Jimenez-Fernandez ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation ◽  
Non Linear ◽  
Linear Problems ◽  
Linear Differential

In this paper, we present modified homotopy perturbation method coupled by Laplace transform to solve non-linear problems. As case study modified homotopy perturbation method coupled by Laplace transform is employed in order to obtain an approximate solution for the non-linear differential equation that describes the steady-state of a heat 1-D flow. The comparison between approximate and exact solutions shows the practical potentiality of the method.

scholarly journals Correctness conditions for high-order differential equations with unbounded coefficients

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kordan N. Ospanov
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Order Linear Differential Equation ◽  
Unbounded Coefficients ◽  
Weighted Norms ◽  
Uniqueness Of The Solution ◽  
Linear Differential

AbstractWe give some sufficient conditions for the existence and uniqueness of the solution of a higher-order linear differential equation with unbounded coefficients in the Hilbert space. We obtain some estimates for the weighted norms of the solution and its derivatives. Using these estimates, we show the conditions for the compactness of some integral operators associated with the resolvent.

Asymptotic behavior of solutions of half-linear differential equations and generalized Karamata functions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kusano Takaŝi ◽  
Jelena V. Manojlović
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Continuous Function ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Regular Variation ◽  
Asymptotic Formulas ◽  
Asymptotic Behavior Of Solutions ◽  
Positive Continuous Function ◽  
Linear Differential

AbstractWe study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation(p(t)\lvert x^{\prime}\rvert^{\alpha}\operatorname{sgn}x^{\prime})^{\prime}+q(% t)\lvert x\rvert^{\alpha}\operatorname{sgn}x=0,where q is a continuous function which may take both positive and negative values in any neighborhood of infinity and p is a positive continuous function satisfying one of the conditions\int_{a}^{\infty}\frac{ds}{p(s)^{1/\alpha}}=\infty\quad\text{or}\quad\int_{a}^% {\infty}\frac{ds}{p(s)^{1/\alpha}}<\infty.The asymptotic formulas for generalized regularly varying solutions are established using the Karamata theory of regular variation.

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