Explosion of limit cycles and chaotic waves in a simple nonlinear chemical system

Explosion of limit cycles and chaotic waves in a simple nonlinear chemical system.

We consider a simple model of an autocatalytic chemical reaction where a limit cycle rapidly increases to infinite period and amplitude, and disappears under variation of a parameter. We show that this bifurcation can be understood from seeing the system as a singular perturbation problem, and we find the bifurcation point by an asymptotic analysis. Scaling laws for period and amplitude are der...

Chaotic dynamic analysis and nonlinear control of blood glucose regulation system in type 1 diabetic patients

In this paper, chaotic dynamic and nonlinear control in a glucose-insulin system in types I diabetic patients and a healthy person have been investigated. Chaotic analysis methods of the blood glucose system include Lyapunov exponent and power spectral density based on the time series derived from the clinical data. Wolf's algorithm is used to calculate the Lyapunov exponent, which positive val...

stable limit cycles generating in a class of uncertain nonlinear systems: application in inertia pendulum

this paper considers the problem of stable limit cycles generating in a class of uncertain nonlinear systems which leads to stable oscillations in the system’s output.this is a wanted behavior in many practical engineering problems. for this purpose, first the equation of the desirable limit cycle is achieved according to shape, amplitude and frequency of the required output oscillations. then,...

On Nonlinear Water Waves in a Channel

Fire and explosion risk assessment in a chemical company by the application of DOW fire and explosion index

Background: Fire and explosion hazards are extremely important in processing units. This study was performed to identify the risk centers, the potential damage caused by fire and explosion, and the days of production cessation in the processing company. Materials and Methods: The present qualitative case study was conducted using Dow’s index in 2015. The fire and explosion hazard index...