scholarly journals On the stability of a periodic solution of distributed parameters biochemical system

2015 ◽  
Vol 432 (1) ◽  
pp. 196-213 ◽  
Author(s):  
Abdou K. Dramé ◽  
Frédéric Mazenc ◽  
Peter R. Wolenski
Keyword(s):  
Periodic Solution ◽  
Biochemical System ◽  
Distributed Parameters ◽  
The Stability

Existence of Periodic Solution for Equation of Motion of Simple Beams With Harmonically Variable Length

1995 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Gholamreza Nakhaie-Jazar ◽  
Bahman Mehri
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Function ◽  
Axial Direction ◽  
Equation Of Motion ◽  
The Other ◽  
Sufficient Condition ◽  
Vibrating String ◽  
The Stability ◽  
Special Case

Abstract The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem. The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

Asymptotic Behavior of Periodic Cohen-Grossberg Neural Networks with Delays

2009 ◽  
Vol 21 (12) ◽  
pp. 3444-3459 ◽  
Author(s):  
Wei Lin
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Lyapunov Method ◽  
Autonomous Systems ◽  
Neural Systems ◽  
Stability Criteria ◽  
Volterra System ◽  
Numerical Examples ◽  
The Stability ◽  
Special Case

Without assuming the positivity of the amplification functions, we prove some M-matrix criteria for the [Formula: see text]-global asymptotic stability of periodic Cohen-Grossberg neural networks with delays. By an extension of the Lyapunov method, we are able to include neural systems with multiple nonnegative periodic solutions and nonexponential convergence rate in our model and also include the Lotka-Volterra system, an important prototype of competitive neural networks, as a special case. The stability criteria for autonomous systems then follow as a corollary. Two numerical examples are provided to show that the limiting equilibrium or periodic solution need not be positive.

scholarly journals Stability and Hopf Bifurcation Analysis of an Epidemic Model by Using the Method of Multiple Scales

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Wanyong Wang ◽  
Lijuan Chen
Keyword(s):  
Periodic Solution ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Epidemic Model ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Value Of Time ◽  
Nonlinear Incidence Rate ◽  
The Stability ◽  
Bifurcating Periodic Solution

A delayed epidemic model with nonlinear incidence rate which depends on the ratio of the numbers of susceptible and infectious individuals is considered. By analyzing the corresponding characteristic equations, the effects of time delay on the stability of the equilibria are studied. By choosing time delay as bifurcation parameter, the critical value of time delay at which a Hopf bifurcation occurs is obtained. In order to derive the normal form of the Hopf bifurcation, an extended method of multiple scales is developed and used. Then, the amplitude of bifurcating periodic solution and the conditions which determine the stability of the bifurcating periodic solution are obtained. The validity of analytical results is shown by their consistency with numerical simulations.

ANALYSIS OF A MODEL OF PLASMID-BEARING, PLASMID-FREE COMPETITION IN A PULSED CHEMOSTAT

2006 ◽  
Vol 09 (03) ◽  
pp. 263-276 ◽  
Author(s):  
XIANGYUN SHI ◽  
XINYU SONG ◽  
XUEYONG ZHOU
Keyword(s):  
Periodic Solution ◽  
Stability Analysis ◽  
Bifurcation Theory ◽  
Continuous System ◽  
Impulsive Effect ◽  
Chemostat Model ◽  
Free Competition ◽  
The Stability ◽  
Invasion Threshold ◽  
Standard Techniques

We introduce and study a chemostat model with plasmid-bearing, plasmid-free competition and impulsive effect. According to the stability analysis of the boundary periodic solution, we obtain the invasion threshold of the plasmid-free organism and plasmid-bearing organism. Furthermore, by using standard techniques of bifurcation theory, we prove the system has a positive τ-periodic solution, which shows that the impulsive effect destroys the equilibria of the unforced continuous system and initiates the periodic solution. Our results can be applied to control bioreactors aimed at producing commercial products through genetically altered organisms.

Conditions of Parametric Resonance in Periodically Time-Variant Systems With Distributed Parameters

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Yong-Kwan Lee ◽  
Leonid S. Chechurin
Keyword(s):  
Parametric Resonance ◽  
Robot Manipulator ◽  
Synchronous Generator ◽  
Constant Current ◽  
Time Varying ◽  
Distributed Parameters ◽  
Time Varying Parameter ◽  
Manipulator Arm ◽  
The Stability ◽  
Systems With Distributed Parameters

Theoretical analysis of the stability problem for the control systems with distributed parameters shall be given. The approach to the analysis of such systems can be composed of two parts. First, the distributed parameter element is modeled by a frequency response function. Second, approximate conditions of parametric resonance are derived by a method of stationarization (describing functions of time-variant elements). The approach is illustrated by two examples. One is a robot-manipulator arm (distributed mechanical parameter system) controlled by a controller with a modulator/demodulator cascade (time-varying element). Another is an electromechanical transformer that consists of a constant current motor and a synchronous generator. Inductance between stator windings and the rotor of the synchronous generator serves as a periodical time-varying parameter, and a long electrical line plays the role of an element with distributed parameters. In both examples, dangerous (in terms of the first parametric resonance) regions for time-varying parameter are obtained theoretically and compared with simulation experiment.

scholarly journals Dynamics Analysis and Biomass Productivity Optimisation of a Microbial Cultivation Process through Substrate Regulation

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Kaibiao Sun ◽  
Shan Liu ◽  
Andrzej Kasperski ◽  
Yuan Tian
Keyword(s):  
Periodic Solution ◽  
Substrate Concentration ◽  
Process Model ◽  
Biomass Productivity ◽  
High Yield ◽  
Dynamics Analysis ◽  
State Dependent ◽  
Cultivation Process ◽  
Microbial Cultivation ◽  
The Stability

A microbial cultivation process model with variable biomass yield, control of substrate concentration, and biomass recycle is formulated, where the biochemical kinetics follows an extension of the Monod and Contois models. Control of substrate concentration allows for indirect monitoring of biomass and dissolved oxygen concentrations and consequently obtaining high yield and productivity of biomass. Dynamics analysis of the proposed model is carried out and the existence of order-1 periodic solution is deduced with a formulation of the period, which provides a theoretical possibility to convert the state-dependent control to a periodic one while keeping the dynamics unchanged. Moreover, the stability of the order-1 periodic solution is verified by a geometric method. The stability ensures a certain robustness of the adopted control; that is, even with an inaccurately detected substrate concentration or a deviation, the system will be always stable at the order-1 periodic solution under the control. The simulations are carried out to complement the theoretical results and optimisation of the biomass productivity is presented.

scholarly journals A Pest Management Model with Stage Structure and Impulsive State Feedback Control

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Guoping Pang ◽  
Zhiqing Liang ◽  
Weijian Xu ◽  
Lijie Li ◽  
Gang Fu
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
Pest Management ◽  
State Feedback ◽  
Stage Structure ◽  
State Feedback Control ◽  
Management Model ◽  
Continuous Systems ◽  
Impulsive State Feedback Control ◽  
The Stability

A pest management model with stage structure and impulsive state feedback control is investigated. We get the sufficient condition for the existence of the order-1 periodic solution by differential equation geometry theory and successor function. Further, we obtain a new judgement method for the stability of the order-1 periodic solution of the semicontinuous systems by referencing the stability analysis for limit cycles of continuous systems, which is different from the previous method of analog of Poincarè criterion. Finally, we analyze numerically the theoretical results obtained.

Methods for Determinning Critical Values of Nonconservative Loads in Problems of Stability of Mechanical Systems

2019 ◽  
pp. 3-13 ◽  
Author(s):  
V.P. Radin ◽  
V.P. Chirkov ◽  
A.V. Shchugorev ◽  
V.N. Shchugorev
Keyword(s):  
Complex Function ◽  
Mechanical Systems ◽  
Critical Values ◽  
The Finite Element Method ◽  
Natural Oscillations ◽  
Flowing Liquid ◽  
Stability Problems ◽  
Distributed Parameters ◽  
The Stability ◽  
Systems With Distributed Parameters

Methods for determining critical values of nonconservative loads in stability problems of mechanical systems with distributed parameters are considered in this work. Based on a dynamic approach to stability problems, the method of direct integration of the linearized equation of perturbed motion is proposed, and the problem of determining critical loads is reduced to the problem of minimizing a complex function of several variables. As a second method, the method of decomposition of the solution of the equation of perturbed motion in the forms of natural oscillations is presented. The fundamentals of the application of the finite element method to the problems of stability under the action of non-conservative loads are also described. The methods are illustrated on classical problems: the stability of the cantilever rod under the action of potential and tracking forces and the stability of the pipeline section with flowing liquid. The accuracy and convergence of the latter two methods are analyzed depending on the number of members in the series and the number of finite elements.

Mathematical Analysis of Stability of a Spinning Disk Under Rotating, Arbitrarily Large Damping Forces

1996 ◽  
Vol 118 (4) ◽  
pp. 657-662 ◽  
Author(s):  
F. Y. Huang ◽  
C. D. Mote
Keyword(s):  
Periodic Solution ◽  
Parameter Space ◽  
Perturbation Technique ◽  
Stability Boundary ◽  
Rotating Disk ◽  
Stable Region ◽  
Damping Force ◽  
Analysis Of Stability ◽  
The Stability ◽  
Nontrivial Periodic Solution

Stability of a rotating disk under rotating, arbitrarily large damping forces is investigated analytically. Points possibly residing on the stability boundary are located exactly in parameter space based on the criterion that at least one nontrivial periodic solution is necessary at every boundary point. A perturbation technique and the Galerkin method are used to predict whether these points of periodic solution reside on the stability boundary, and to identify the stable region in parameter space. A nontrivial periodic solution is shown to exist only when the damping does not generate forces with respect to that solution. Instability occurs when the wave speed of a mode in the uncoupled disk, when observed on the disk, is exceeded by the rotation speed of the damping force relative to the disk. The instability is independent of the magnitude of the force and the type of positive-definite damping operator in the applied region. For a single dashpot, nontrivial periodic solutions exist at the points where the uncoupled disk has repeated eigenfrequencies on a frame rotating with the dashpot and the dashpot neither damps nor energizes these modes substantially around these points.

OSCILLATION DEATH IN A TWO-NEURON NETWORK WITH DELAY IN A SELF-CONNECTION

2007 ◽  
Vol 15 (01) ◽  
pp. 49-61 ◽  
Author(s):  
L. H. A. MONTEIRO ◽  
A. PELLIZARI FILHO ◽  
J. G. CHAUI-BERLINCK ◽  
J. R. C. PIQUEIRA
Keyword(s):  
Periodic Solution ◽  
Time Delay ◽  
Olfactory Bulb ◽  
Trivial Solution ◽  
Dynamical Behavior ◽  
Neuron Network ◽  
The Stability

We analytically study the dynamical behavior of a two-neuron network with a time-delayed self-connection. The effect of the time delay on the stability of the trivial solution and on the existence of self-sustained periodic solution are investigated. These results could be applied to understand the temporal activity appearing in the olfactory bulb.

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