Periodic solution to a kind of singularly perturbed differential equations of parabolic type in chemical kinetics

1991 ◽  
Vol 12 (5) ◽  
pp. 461-468
Author(s):  
Ni Ming-kang
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Chemical Kinetics ◽  
Parabolic Type ◽  
Singularly Perturbed

scholarly journals Periodic Solutions in Slowly Varying Discontinuous Differential Equations: The Generic Case

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2449
Author(s):  
Flaviano Battelli ◽  
Michal Fečkan
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Singularly Perturbed ◽  
Two Dimensional ◽  
Singularly Perturbed Equation ◽  
Discontinuous Differential Equations ◽  
Scalar Variable ◽  
Perturbed Equation

We study persistence of periodic solutions of perturbed slowly varying discontinuous differential equations assuming that the unperturbed (frozen) equation has a non singular periodic solution. The results of this paper are motivated by a result of Holmes and Wiggins where the authors considered a two dimensional Hamiltonian family of smooth systems depending on a scalar variable which is the solution of a singularly perturbed equation.

Certain problems with the application of stochastic diffusion processes for description of chemical engineering phenomena; Kolmogorov and classic diffusion equations

1988 ◽  
Vol 53 (6) ◽  
pp. 1181-1197
Author(s):  
Vladimír Kudrna
Keyword(s):  
Mass Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Parabolic Type ◽  
Diffusion Equations ◽  
Stochastic Motion ◽  
Energy Component ◽  
Classic Form

The paper presents alternative forms of partial differential equations of the parabolic type used in chemical engineering for description of heat and mass transfer. It points at the substantial difference between the classic form of the equations, following from the differential balances of mass and enthalpy, and the form following from the concept of stochastic motion of particles of mass or energy component. Examples are presented of the processes that may be described by the latter method. The paper also reviews the cases when the two approaches become identical.

NUMERICAL COMPUTATION OF CANARDS

2000 ◽  
Vol 10 (12) ◽  
pp. 2669-2687 ◽  
Author(s):  
JOHN GUCKENHEIMER ◽  
KATHLEEN HOFFMAN ◽  
WARREN WECKESSER
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Electrical Potential ◽  
Slow Manifold ◽  
Singularly Perturbed ◽  
Singularly Perturbed Systems ◽  
Singularly Perturbed System ◽  
Chemical Systems ◽  
Perturbed System ◽  
Physical And Chemical

Singularly perturbed systems of ordinary differential equations arise in many biological, physical and chemical systems. We present an example of a singularly perturbed system of ordinary differential equations that arises as a model of the electrical potential across the cell membrane of a neuron. We describe two periodic solutions of this example that were numerically computed using continuation of solutions of boundary value problems. One of these periodic orbits contains canards, trajectory segments that follow unstable portions of a slow manifold. We identify several mechanisms that lead to the formation of these and other canards in this example.

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