scholarly journals Parameter Identification For Oscillating Chemical Reactions Modelled By Systems Of Ordinary Differential Equations

2003 ◽  
Vol 3 (2) ◽  
pp. 223-232
Author(s):  
L.K. Babadzanjanz ◽  
J.A. Boyle ◽  
D.R. Sarkissian ◽  
J. Zhu
Keyword(s):  
Differential Equations ◽  
Parameter Identification ◽  
Ordinary Differential Equations ◽  
Chemical Reactions

SELF-SIMILAR PROBLEMS FOR MODELING THE SURFACE CHEMICAL REACTIONS WITH THE GRAVITATION

1998 ◽  
Vol 3 (1) ◽  
pp. 25-32
Author(s):  
Jânis Cepîtis ◽  
Harijs Kalis
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Chemical Reactions ◽  
Glass Fibre ◽  
Surface Chemical ◽  
Self Similar ◽  
Surface Chemical Reactions ◽  
The Mathematical Model

The mathematical model of a chemical reaction which takes place on the surface of the uniformly moving vertically imbedded glass fibre material is considered. The effect of gravitation is taken into account. Boussinesq's and boundary layer fittings allow to derive boundary value problems for self‐similar systems of ordinary differential equations.

scholarly journals Nonlinear Parameter Identification for Ordinary Differential Equations

PAMM ◽  
2013 ◽  
Vol 13 (1) ◽  
pp. 457-458 ◽  
Author(s):  
Mitja Wöbbekind ◽  
Anna Kemper ◽  
Christof Büskens ◽  
Michael Schollmeyer
Keyword(s):  
Differential Equations ◽  
Parameter Identification ◽  
Ordinary Differential Equations ◽  
Nonlinear Parameter ◽  
Nonlinear Parameter Identification

scholarly journals CHAOTIC OSCILLATIONS IN SIMPLEST CHEMICAL REACTION

2018 ◽  
Vol 61 (4-5) ◽  
pp. 133
Author(s):  
Nikolay I. Kol'tsov
Keyword(s):  
Kinetic Model ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Dynamic Model ◽  
Lyapunov Exponents ◽  
Chemical Reactions ◽  
Chemical Reaction ◽  
Kinetic Models ◽  
Intermediate Stage ◽  
Chaotic Oscillations

It is known that chaotic oscillations for chemical reactions can be described by non-stationary kinetic models consisting of three ordinary differential equations.  Rossler established the first examples of chemical reactions, including the two-route five-stage reaction of the Villamovski-Rossler, with three intermediate substances, containing three autocatalytic on intermediates stages, the dynamic model of which describes chaotic oscillations. In given article presents a simple one-route four-stages reaction A+E=D involving two autocatalytic and one linear on intermediate stage, the non-stationary kinetic model of which describes chaotic oscillations. The non-stationary kinetic model under the assumption of quasistationarity with respect to the main substances within the framework of the law of acting masses is a system of three ordinary differential equations. The presence of chaos is confirmed by numerical calculations of the kinetic model and Lyapunov exponentials. The Lyapunov exponents satisfy the condition L1+L2+L3<0, which proves the existence of chaotic oscillations.Forcitation:Kol'tsov N.I. Chaotic oscillations in simplest chemical reaction. Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol. 2018. V. 61. N 4-5. P. 133-135

INTERPRETATION OF POPULATION DYNAMICS MODELS BY USING SCHEMATIC REPRESENTATIONS

1993 ◽  
Vol 01 (03) ◽  
pp. 275-309 ◽  
Author(s):  
A. PAVÉ
Keyword(s):  
Population Dynamics ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Chemical Reactions ◽  
Biological Mechanisms ◽  
Predator Prey ◽  
Competition Models ◽  
Population Dynamics Models ◽  
Dynamics Models ◽  
Kinetics Of

A framework for interpretation of classical populations dynamics models written in terms of ordinary differential equations and related to biological mechanisms is proposed. This approach is based on the construction of functional schemes, similar to those used to symbolize chemical reactions. These schemes can be associated to differential equations which formalize the kinetics of these reactions. So schemes associated to classical one-species models are given (exponential, logistic, Gompertz, and Kostitzin models). Some typical cases of two species models proposed by Lotka and Volterra (predator-prey and competition models) are also explored.

scholarly journals Exact Reduction of the Generalized Lotka–Volterra Equations via Integral and Algebraic Substitutions

Computation ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 49
Author(s):  
Rebecca E. Morrison
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Chemical Reactions ◽  
Reduction Process ◽  
Approximate Model ◽  
Reduced Model ◽  
Volterra Equations ◽  
Coupled Dynamics ◽  
Interacting Species ◽  
Promising Type

Systems of interacting species, such as biological environments or chemical reactions, are often described mathematically by sets of coupled ordinary differential equations. While a large number β of species may be involved in the coupled dynamics, often only α<β species are of interest or of consequence. In this paper, we explored how to construct models that include only those given α species, but still recreate the dynamics of the original β-species model. Under some conditions detailed here, this reduction can be completed exactly, such that the information in the reduced model is exactly the same as the original one, but over fewer equations. Moreover, this reduction process suggests a promising type of approximate model—no longer exact, but computationally quite simple.

THE PARAMETER IDENTIFICATION PROBLEM FOR SYSTEM OF DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 73 (1) ◽  
pp. 7-12
Author(s):  
A.T. Assanova ◽  
◽  
Ye. Shynarbek ◽  
Keyword(s):  
Differential Equations ◽  
Parameter Identification ◽  
Ordinary Differential Equations ◽  
Unique Solvability ◽  
Identification Problem ◽  
Identification Problems ◽  
Parameter Identification Problem ◽  
Parameter Identification Problems ◽  
And Control ◽  
Differential Part

In this paper, the parameter identification problem for system of ordinary differential equations is considered. The parameter identification problem for system of ordinary differential equations is investigated by the Dzhumabaev’s parametrization method. At first, conditions for a unique solvability of the parameter identification problem for system of ordinary differential equations are obtained in the term of fundamental matrix of system’s differential part. Further, we establish conditions for a unique solvability of the parameter identification problem for system of ordinary differential equations in the terms of initial data. Algorithm for finding of approximate solution to a unique solvability of the parameter identification problem for system of ordinary differential equations is proposed and the conditions for its convergence are setted. Results this paper can be use for investigating of various problems with parameter and control problems for system of ordinary differential equations. The approach in this paper can be apply to the parameter identification problems for partial differential equations.

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