Dynamics of a delayed competitive system affected by toxic substances with imprecise biological parameters

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5271-5293
Author(s):  
A.K. Pal ◽  
P. Dolai ◽  
G.P. Samanta
Keyword(s):  
Equilibrium Points ◽  
Stable Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Toxic Substances ◽  
Stable Limit ◽  
Biological Parameters ◽  
Delay Model ◽  
Competitive System ◽  
Interval Numbers ◽  
Cycle Oscillation

In this paper we have studied the dynamical behaviours of a delayed two-species competitive system affected by toxicant with imprecise biological parameters. We have proposed a method to handle these imprecise parameters by using parametric form of interval numbers. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. In case of toxic stimulatory system, the delay model exhibits a stable limit cycle oscillation. Computer simulations are carried out to illustrate our analytical findings.

Stability analysis of a delayed predator–prey model with nonlinear harvesting efforts using imprecise biological parameters

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Amit K. Pal
Keyword(s):  
Equilibrium Points ◽  
Stable Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Stable Limit ◽  
Biological Parameters ◽  
Delay Model ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Nonlinear Harvesting

Abstract In this paper, the dynamical behaviors of a delayed predator–prey model (PPM) with nonlinear harvesting efforts by using imprecise biological parameters are studied. A method is proposed to handle these imprecise parameters by using a parametric form of interval numbers. The proposed PPM is presented with Crowley–Martin type of predation and Michaelis–Menten type prey harvesting. The existence of various equilibrium points and the stability of the system at these equilibrium points are investigated. Analytical study reveals that the delay model exhibits a stable limit cycle oscillation. Computer simulations are carried out to illustrate the main analytical findings.

Static/Dynamic Edge Movability Effect on Non-Linear Aerothermoelastic Behavior of Geometrically Imperfect Curved Skin Panel: Flutter and Post-Flutter Analysis

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
Laith K. Abbas ◽  
Xiaoting Rui ◽  
P. Marzocca ◽  
M. Abdalla ◽  
R. De Breuker
Keyword(s):  
Stable Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Stable Limit ◽  
Third Order ◽  
Curved Panel ◽  
Flutter Analysis ◽  
Non Linear ◽  
Cycle Oscillation ◽  
Modeling Behavior ◽  
Curved Panels

This paper addresses the problem of the aerothermoelastic modeling behavior and analyses of skin curved panels with static and dynamic edge movability effect in high supersonic flow. Flutter and post-flutter behavior will be analyzed toward determining under which conditions such panels will exhibit a benign instability, that is a stable limit cycle oscillation, or a catastrophic instability, that is an unstable LCO. The aerothermoelastic governing equations are developed from the geometrically non-linear theory of infinitely long two dimensional curved panels. Von Kármán non-linear strain-displacement relation in conjunction with the Kirchhoff plate-hypothesis is adopted. A geometrically imperfect curved panel forced by a supersonic/hypersonic unsteady flow is numerically investigated using Galerkin approach. These equations are based on the third-order piston theory aerodynamic for modeling the flow-induced forces. Furthermore, the effects of thermal degradation and Kelvin’s model of structural damping independent of time and temperature are also considered in this model. Computational analysis and discussion of the finding along with pertinent conclusions are presented.

Limit-Cycle Oscillation Suppression of Bioinspired Ornithopter: Wind Tunnel Testing

2011 ◽  
Author(s):  
Jun-Seong Lee ◽  
Dong-Kyu Lee ◽  
Juho Lee ◽  
Jae-Hung Han
Keyword(s):  
Wind Tunnel ◽  
Limit Cycle ◽  
Fiber Composite ◽  
Elevation Angle ◽  
Stable Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Stable Limit ◽  
Wing Motion ◽  
Cycle Oscillation ◽  
Trim Flight

This study experimentally shows that an oscillatory behavior observed in a trim flight of an ornithopter has a stable limit-cycle oscillation (LCO) characteristics and that the magnitude of the LCO in body pitch dynamics can be suppressed by active tail motion. A free flight of the tested ornithopter is emulated in the wind tunnel using a specially devised tether that provides the minimal mechanical interference to the flight of ornithopter. Due to the symmetric wing motion in forward trim flight, the longitudinal flight dynamics is more focused than the lateral one. The non-contact type sensors are used to measure the time histories of the flight state variables such as wing and tail motions, body pitch angle, and altitude. The tail motion for the pitch LCO reduction is achieved by two actuators: 1) Servo motor for the rigid-body motion of the tail elevation angle, and 2) Macro-Fiber Composite strain actuator for the elastic deformation of the tail camber. The performances of the LCO suppressions are compared in the root-mean-square-error sense and the harmonically activated in-phase tail motion linked to wing motion is observed to effectively reduce the pitch LCO.

Applicability of Harmonic Balance for the Determination of Blade Stability Within the Prescribed Motion Approach

2020 ◽  
Author(s):  
Virginie Anne Chenaux ◽  
Matthias Schuff ◽  
David Quero
Keyword(s):  
Time Domain ◽  
Harmonic Balance ◽  
Duffing Oscillator ◽  
Stable Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Stable Limit ◽  
Nonlinear Frequency ◽  
Compressor Rotor ◽  
New Development ◽  
Cycle Oscillation

Abstract To predict blade aerodynamic damping during the design phase, unsteady linearized CFD methods are commonly used as they offer a reasonable accuracy at acceptable computational costs. However, for moderate blade oscillation amplitudes, nonlinear aerodynamic effects may appear, yielding eventually an evolution into a stable, limit cycle oscillation (LCO). In the perspective of raising performance and safety, identifying such scenarios might open new development possibilities. Therefore, a valuable alternative to expensive CFD time domain methods consists in applying the nonlinear frequency domain harmonic balance (HB) approach to determine the aerodynamic response. An appropriate number of higher harmonics have to be retained depending on the severity of the aerodynamic nonlinearity under consideration. This number can be identified using either a convergence study with an increasing number of harmonics, or a direct comparison with time-domain simulations. For weak to moderate aerodynamic nonlinearities, this work proposes a guideline to determine the number of harmonics without additional, comparative simulations. First, the HB convergence properties are derived using the well-known Duffing oscillator. Next, the method is applied to a compressor rotor blade subjected to a prescribed harmonic motion for conditions with and without aerodynamic nonlinearities.

Developing a Reduced-Order Model to Understand Non-Synchronous Vibration (NSV) in Turbomachinery

2012 ◽  
Author(s):  
Stephen T. Clark ◽  
Robert E. Kielb ◽  
Kenneth C. Hall
Keyword(s):  
Stable Limit Cycle ◽  
Forced Response ◽  
Van Der Pol Oscillator ◽  
Future Research ◽  
Limit Cycle Oscillation ◽  
Preliminary Design ◽  
Stable Limit ◽  
Van Der Pol ◽  
Reduced Order ◽  
Van Der Pol Model

This paper demonstrates the potential of using a multi-degree-of-freedom, traditional van der Pol oscillator to model Non-Synchronous Vibration (NSV) in turbomachinery. It is shown that the two main characteristics of NSV are captured by the reduced-order, van der Pol model. First, a stable limit cycle oscillation (LCO) is maintained for various conditions. Second, the lock-in phenomenon typical of NSV is captured for various fluid-structure frequency ratios. The results also show the maximum amplitude of the LCO occurs at an off-resonant condition, i.e., when the natural shedding frequency of the aerodynamic instability is not coincident with the natural modal frequency of the structure. This conclusion is especially relevant in preliminary design in industry because it suggests that design engineers cannot treat NSV as a normal Campbell-diagram crossing as they would for preliminary design for forced response; it is possible that by redesigning the blade, the response amplitude of the blade may actually be higher. The goal of future research will be to identify values and significance of the coupling parameters used in the van der Pol model, to match these coefficients with confirmed instances of experimental NSV, and to develop a preliminary design tool that engineers can use to better design turbomachinery for NSV. Proper Orthogonal Decomposition (POD) CFD techniques and coefficient tuning from experimental instances of NSV have been considered to identify the unknown coupling coefficients in the van der Pol model. Both the modeling of experimental NSV and preliminary design development will occur in future research.

scholarly journals Stability analysis of shock response of EV powertrain considering electro-mechanical coupling effect

2021 ◽  
Vol 13 (8) ◽  
pp. 168781402110371
Author(s):  
Qingzhen Han ◽  
Shiqin Niu ◽  
Jie You
Keyword(s):  
Coupling Effect ◽  
Equilibrium Points ◽  
Stable Limit Cycle ◽  
Central Point ◽  
Stable Limit ◽  
Mechanical Coupling ◽  
Saddle Node ◽  
Shock Response ◽  
Response Equation ◽  
The Stability

The main purpose of this manuscript is to analyze the stability of the shock response of the electric vehicle (EV) powertrain when considering the electro-mechanical coupling effect. The nonlinear drive-shaft model of the powertrain is built using the Lagrange method, based on which the shock response equation is also deduced. Meanwhile, the number and properties of the equilibrium points are studied. Two kinds of equilibrium points, saddle node and central point, which can induce different dynamic behaviors are found. The simulation results show that the trajectory of the shock response may be unstable if the parameters are chosen in the region that has a saddle node. If the parameters of the powertrain fall into the region that has only one central point, the trajectory of the shock response will be attracted by the stable limit cycle. Therefore, to ensure that the shock response is more stable, the parameters should be chosen in the region where only one central point is present.

OSCILLATIONS IN DELAY DIFFERENTIAL EQUATION MODEL OF REPRODUCTIVE HORMONES IN MEN WITH COMPUTER SIMULATIONS

1994 ◽  
Vol 02 (01) ◽  
pp. 73-90 ◽  
Author(s):  
PRITHA DAS ◽  
A.B. ROY
Keyword(s):  
Stable Limit Cycle ◽  
Equation Model ◽  
Reproductive Hormones ◽  
Phase Portraits ◽  
Stable Limit ◽  
Delay Model ◽  
Local Asymptotic Stability ◽  
The Stability ◽  
Linearized Model ◽  
Delay Differential

We produce here a delay model to explain the control of testosterone secretion. We have modified our earlier model by incorporating one negative feedback function which explains the inhibition of the pituitary secretion of the hormone LH (Luteinizing hormone) by the local testosterone concentration. We have derived the conditions for local asymptotic stability and switching to instability of the steady state. The length of the delay preserving the stability has also been derived. Lastly the conditions for instability and bifurcation results have been derived for the linearized model. Phase portraits of the original nonlinear model showing stable limit cycle have been simulated.

Stability analysis of combined project of fish, broiler and ducks: Dynamical system in imprecise environment

2015 ◽  
Vol 08 (05) ◽  
pp. 1550067 ◽  
Author(s):  
A. De ◽  
K. Maity ◽  
M. Maiti
Keyword(s):  
Dynamical System ◽  
Mathematical Program ◽  
Equilibrium Points ◽  
Solution Procedure ◽  
Biological Parameters ◽  
Mathematical Software ◽  
Interval Numbers ◽  
Different Characteristics ◽  
Interval Valued ◽  
Biological Equilibrium

In this paper, we consider three species harvesting model and develop a solution procedure which is able to calculate the equilibrium points of the model where some biological parameters of the model are interval numbers. A parametric mathematical program is formulated to find the biological equilibrium of the model for different values of parameters. This interval-valued problem is converted into equivalent crisp model using interval operations. The main advantage of the proposed procedure is that we can present different characteristics of the model in a single framework. Analytically, the existence of steady state and stabilities are looked into. Using mathematical software, the model is illustrated and the results are obtained and presented in tabular and graphical forms.

Sign in / Sign up

Export Citation Format

Share Document