scholarly journals Qualitative Properties of Autocatalytic Reactions Occurring in a Flow System

1985 ◽  
Vol 40 (7) ◽  
pp. 736-747
Author(s):  
Sang H. Kim ◽  
Vladimir Hlavacek
Keyword(s):  
Chaotic Behavior ◽  
Flow System ◽  
Cell Model ◽  
Dispersion Model ◽  
Travelling Waves ◽  
Continuous Model ◽  
Product Inhibition ◽  
Stable Node ◽  
Qualitative Properties ◽  
Intermediate Value

The dynamic behavior of an autocatalytic reaction with a product inhibition term is studied in a flow system. A unique steady state exists in the continuous tank reactor. Linear stability analysis predicts either a stable node, a focus or an unstable saddle-focus. Sustained oscillations around the unstable focus can occur for high values of the Damköhler number (Da). In the distributed system, travelling, standing or complex oscillatory waves are detected. For a low value of Da, travelling waves with a pseudo-constant pattern are observed. With an intermediate value of Da, single or multiple standing waves are obtained. The temporal behavior indicates also the appearance of retriggering or echo waves. For a high value of Da, both single peak and complex multipeak oscillations are found. In the cell model, both regular oscillations near the inlet and chaotic behavior downstream are observed. In the dispersion model, higher Peclet numbers (Pe) eliminate the oscillations. The spatial profile shows a train of pulsating waves for the discrete model and a single pulsating or solitary wave for the continuous model.

scholarly journals Geometric Numerical Integration in Ecological Modelling

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 25 ◽  
Author(s):  
Fasma Diele ◽  
Carmela Marangi
Keyword(s):  
Numerical Integration ◽  
Time Integration ◽  
Continuous Model ◽  
Ecological Models ◽  
Ecological Modelling ◽  
Geometric Numerical Integration ◽  
Qualitative Properties ◽  
Long Time ◽  
Numerical Integrators ◽  
Long Time Integration

A major neglected weakness of many ecological models is the numerical method used to solve the governing systems of differential equations. Indeed, the discrete dynamics described by numerical integrators can provide spurious solution of the corresponding continuous model. The approach represented by the geometric numerical integration, by preserving qualitative properties of the solution, leads to improved numerical behaviour expecially in the long-time integration. Positivity of the phase space, Poisson structure of the flows, conservation of invariants that characterize the continuous ecological models are some of the qualitative characteristics well reproduced by geometric numerical integrators. In this paper we review the benefits induced by the use of geometric numerical integrators for some ecological differential models.

scholarly journals Campbell diagrams of weakly anisotropic flexible rotors

2009 ◽  
Vol 465 (2109) ◽  
pp. 2703-2723 ◽  
Author(s):  
O. N. Kirillov
Keyword(s):  
Wave Propagation ◽  
Degrees Of Freedom ◽  
Travelling Waves ◽  
Continuous Model ◽  
Unperturbed System ◽  
Rotating Shaft ◽  
Campbell Diagram ◽  
Flexible Rotors ◽  
Complex Eigenvalues ◽  
Subcritical Speed

We consider an axi-symmetric flexible rotor perturbed by dissipative, conservative and non-conservative positional forces originated at the contact with the anisotropic stator. The Campbell diagram of the unperturbed system is a mesh-like structure in the frequency–speed plane with double eigenfrequencies at the nodes. The diagram is convenient for the analysis of the travelling waves in the rotating elastic continuum. Computing sensitivities of the doublets, we find that at every particular node the unfolding of the mesh into the branches of complex eigenvalues in the first approximation is generically determined by only four 2×2 sub-blocks of the perturbing matrix. Selection of the unstable modes that cause self-excited vibrations in the subcritical speed range is governed by the exceptional points at the corners of the singular eigenvalue surfaces—‘double coffee filter’ and ‘viaduct’—which are sharply associated with the crossings of the unperturbed Campbell diagram with the definite symplectic (Krein) signature. The singularities connect the problems of wave propagation in the rotating continua with that of electromagnetic and acoustic wave propagation in non-rotating anisotropic chiral media. As mechanical examples a model of a rotating shaft with two degrees of freedom and a continuous model of a rotating circular string passing through the eyelet are studied in detail.

Multistability and Hidden Attractors in the Dynamics of Permanent Magnet Synchronous Motor

2019 ◽  
Vol 29 (04) ◽  
pp. 1950056 ◽  
Author(s):  
Jay Prakash Singh ◽  
Binoy Krishna Roy ◽  
Nikolay V. Kuznetsov
Keyword(s):  
Permanent Magnet ◽  
Sliding Mode ◽  
Chaotic Behavior ◽  
Permanent Magnet Synchronous Motor ◽  
Synchronous Motor ◽  
Adaptive Sliding Mode Control ◽  
Stable Node ◽  
Control Input ◽  
Hidden Attractors ◽  
Load Torque

This paper attempts to find some interesting and unique properties in the dynamics of a permanent magnet synchronous motor (PMSM). When compared with the existing literature on the dynamics of a PMSM, we find some interesting and unique behaviors which have not been reported so far. These are (i) occurrence of multistability, (ii) existence of hidden attractors and (iii) equilibrium point with two stable node-foci and one saddle point index-1. The above-said unique behaviors in the dynamics of a PMSM are not found in the literature to the best of authors’ knowledge. Three different cases with (a) [Formula: see text] (voltage/frequency) control, (b) constant load torque and (c) constant direct and quadrature-axis voltage, and load torque are considered to show the multistability in the dynamics of a PMSM. The multistability is confirmed by using the bifurcation analysis. In another case, when the load torque is selected as a feedback of quadrature-axis voltage, the system depicts hidden attractors (point, periodic and transient chaotic). An adaptive sliding mode control is designed to control the hidden transient chaotic behavior of the system. The simulation results confirm the suppression of the transient chaotic attractors with smaller stabilization time and chattering free control input.

Chaotic Behavior of a Generalized Sprott E Differential System

2016 ◽  
Vol 26 (05) ◽  
pp. 1650083 ◽  
Author(s):  
Regilene Oliveira ◽  
Claudia Valls
Keyword(s):  
Differential System ◽  
Limit Cycles ◽  
Autonomous System ◽  
Chaotic Behavior ◽  
Stable Node ◽  
Stable Limit ◽  
Poincaré Compactification ◽  
Polynomial Differential System ◽  
Point Attractor ◽  
Two Parameters

A chaotic system with only one equilibrium, a stable node-focus, was introduced by Wang and Chen [2012]. This system was found by adding a nonzero constant [Formula: see text] to the Sprott E system [Sprott, 1994]. The coexistence of three types of attractors in this autonomous system was also considered by Braga and Mello [2013]. Adding a second parameter to the Sprott E differential system, we get the autonomous system [Formula: see text] where [Formula: see text] are parameters and [Formula: see text]. In this paper, we consider theoretically some global dynamical aspects of this system called here the generalized Sprott E differential system. This polynomial differential system is relevant because it is the first polynomial differential system in [Formula: see text] with two parameters exhibiting, besides the point attractor and chaotic attractor, coexisting stable limit cycles, demonstrating that this system is truly complicated and interesting. More precisely, we show that for [Formula: see text] sufficiently small this system can exhibit two limit cycles emerging from the classical Hopf bifurcation at the equilibrium point [Formula: see text]. We also give a complete description of its dynamics on the Poincaré sphere at infinity by using the Poincaré compactification of a polynomial vector field in [Formula: see text], and we show that it has no first integrals in the class of Darboux functions.

scholarly journals A Numerical Comparison for a Discrete HIV Infection of CD4+T-Cell Model Derived from Nonstandard Numerical Scheme

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Mevlüde Yakıt Ongun ◽  
İlkem Turhan
Keyword(s):  
Asymptotic Stability ◽  
Hiv Infection ◽  
Numerical Scheme ◽  
Cell Model ◽  
Continuous Model ◽  
Numerical Comparison ◽  
Time Model ◽  
Stability Properties ◽  
Local Asymptotic Stability ◽  
Linearized Stability

A nonstandard numerical scheme has been constructed and analyzed for a mathematical model that describes HIV infection of CD4+T cells. This new discrete system has the same stability properties as the continuous model and, particularly, it preserves the same local asymptotic stability properties. Linearized Stability Theory and Schur-Cohn criteria are used for local asymptotic stability of this discrete time model. This proposed nonstandard numerical scheme is compared with the classical explicit Euler and fourth order Runge-Kutta methods. To show the efficiency of this numerical scheme, the simulated results are given in tables and figures.

scholarly journals Generalized semi-opened axial dispersion model

2012 ◽  
Vol 22 (1) ◽  
pp. 59-75 ◽  
Author(s):  
Darina Bártová ◽  
Bohumil Jakeš ◽  
Jaromír Kukal
Keyword(s):  
Flow System ◽  
Dispersion Model ◽  
Axial Dispersion ◽  
Input Concentration ◽  
Left Boundary ◽  
Computer Realization ◽  
Mathematical Solution ◽  
Open Flow ◽  
Axial Dispersion Model ◽  
New Form

Generalized semi-opened axial dispersion modelThe axial dispersion model (ADM) is studied and then generalized by a new form of the left boundary condition of semi-open flow system. The resulting parameter driven model covers the traditional axial models: axial closed-opened dispersion model with enforced input concentration (AEO), axial closed-opened dispersion model with input Danckwerts' condition (ACO), and axial opened-opened model (AOO). It also enables development of the degraded axial model (ADO). The research is concerned with both modeling and mathematical solution. Also, many numerical aspects of computer realization are discussed.

General solution of the dispersion model for a one-dimensional stirred flow system using Danckwerts’ boundary conditions

2004 ◽  
Vol 59 (14) ◽  
pp. 3013-3020 ◽  
Author(s):  
Vladimı́r Kudrna ◽  
Milan Jahoda ◽  
Njabulo Siyakatshana ◽  
Jiřina Čermáková ◽  
Václav Machoň
Keyword(s):  
General Solution ◽  
Boundary Conditions ◽  
Flow System ◽  
Dispersion Model ◽  
One Dimensional

Endogenous hydrogen sulfide sulfhydrates IKKβ at cysteine 179 to control pulmonary artery endothelial cell inflammation

2019 ◽  
Vol 133 (20) ◽  
pp. 2045-2059 ◽  
Author(s):  
Da Zhang ◽  
Xiuli Wang ◽  
Siyao Chen ◽  
Selena Chen ◽  
Wen Yu ◽  
...  
Keyword(s):  
Hydrogen Sulfide ◽  
Endothelial Cell ◽  
Pulmonary Artery ◽  
Cell Model ◽  
Site Directed Mutagenesis ◽  
Critical Event ◽  
Hypertensive Rats ◽  
Pulmonary Artery Endothelial Cell

Abstract Background: Pulmonary artery endothelial cell (PAEC) inflammation is a critical event in the development of pulmonary arterial hypertension (PAH). However, the pathogenesis of PAEC inflammation remains unclear. Methods: Purified recombinant human inhibitor of κB kinase subunit β (IKKβ) protein, human PAECs and monocrotaline-induced pulmonary hypertensive rats were employed in the study. Site-directed mutagenesis, gene knockdown or overexpression were conducted to manipulate the expression or activity of a target protein. Results: We showed that hydrogen sulfide (H2S) inhibited IKKβ activation in the cell model of human PAEC inflammation induced by monocrotaline pyrrole-stimulation or knockdown of cystathionine γ-lyase (CSE), an H2S generating enzyme. Mechanistically, H2S was proved to inhibit IKKβ activity directly via sulfhydrating IKKβ at cysteinyl residue 179 (C179) in purified recombinant IKKβ protein in vitro, whereas thiol reductant dithiothreitol (DTT) reversed H2S-induced IKKβ inactivation. Furthermore, to demonstrate the significance of IKKβ sulfhydration by H2S in the development of PAEC inflammation, we mutated C179 to serine (C179S) in IKKβ. In purified IKKβ protein, C179S mutation of IKKβ abolished H2S-induced IKKβ sulfhydration and the subsequent IKKβ inactivation. In human PAECs, C179S mutation of IKKβ blocked H2S-inhibited IKKβ activation and PAEC inflammatory response. In pulmonary hypertensive rats, C179S mutation of IKKβ abolished the inhibitory effect of H2S on IKKβ activation and pulmonary vascular inflammation and remodeling. Conclusion: Collectively, our in vivo and in vitro findings demonstrated, for the first time, that endogenous H2S directly inactivated IKKβ via sulfhydrating IKKβ at Cys179 to inhibit nuclear factor-κB (NF-κB) pathway activation and thereby control PAEC inflammation in PAH.

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