scholarly journals Global Behaviors of a Chemostat Model with Delayed Nutrient Recycling and Periodically Pulsed Input

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Kai Wang ◽  
Zhidong Teng ◽  
Fengqin Zhang
Keyword(s):  
Function Method ◽  
Global Attractivity ◽  
Necessary Conditions ◽  
Nutrient Recycling ◽  
Liapunov Function ◽  
Sufficient Condition ◽  
Chemostat Model ◽  
Dynamic Behaviors ◽  
Analysis Technique ◽  
Sufficient And Necessary Conditions

The dynamic behaviors in a chemostat model with delayed nutrient recycling and periodically pulsed input are studied. By introducing new analysis technique, the sufficient and necessary conditions on the permanence and extinction of the microorganisms are obtained. Furthermore, by using the Liapunov function method, the sufficient condition on the global attractivity of the model is established. Finally, an example is given to demonstrate the effectiveness of the results in this paper.

scholarly journals Dynamic Behaviors of a Nonautonomous Impulsive Competitive System with the Effect of Toxic Substance

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Lijuan Chen ◽  
Fengde Chen ◽  
Liujuan Chen
Keyword(s):  
Global Attractivity ◽  
Toxic Substance ◽  
The Other ◽  
Sufficient Condition ◽  
Toxic Substances ◽  
Competitive System ◽  
Dynamic Behaviors ◽  
Paper Supplement

We firstly propose a nonautonomous impulsive Lotka-Volterra competitive system with the effect of toxic substance. Only one of the two species could produce toxic substance. Sufficient condition which guarantees the extinction of one of the species and the global attractivity of the other species is obtained. We also present an example to verify our main results, which show that species still is possibly driven to extinction when only one of the two species produces toxic substances. The results of this paper supplement the existing results.

ON THE OBSERVABILITY OF CONTINUOUS-TIME DYNAMIC FUZZY CONTROL SYSTEMS

2007 ◽  
Vol 15 (01) ◽  
pp. 75-91
Author(s):  
YUHU FENG ◽  
MIN CHEN ◽  
LIANGJIAN HU
Keyword(s):  
Fuzzy Control ◽  
Control Systems ◽  
Continuous Time ◽  
Necessary Conditions ◽  
Rule Base ◽  
Sufficient Condition ◽  
Initial Value ◽  
Time Dynamic ◽  
Sufficient And Necessary Conditions ◽  
Logic Description

This paper studies the observability of the initial value of continuous-time dynamic fuzzy control systems. The sufficient and necessary conditions for the initial value of fuzzy control system to be observable are given. A concept called strong observability is introduced and a sufficient condition for the initial value of system to be strongly observable is discussed. The fuzzy logic description of input-output relations using IF-THEN rule base is presented.

TWO PATCHES IMPULSIVE DIFFUSION PERIODIC SINGLE-SPECIES LOGISTIC MODEL

2010 ◽  
Vol 03 (01) ◽  
pp. 127-141 ◽  
Author(s):  
ZIJIAN LIU ◽  
ZHIDONG TENG ◽  
LONG ZHANG
Keyword(s):  
Periodic Solution ◽  
Iterative Method ◽  
Numerical Simulations ◽  
Logistic Model ◽  
Global Attractivity ◽  
Necessary Conditions ◽  
Positive Periodic Solution ◽  
Single Species ◽  
Impulsive Diffusion ◽  
Sufficient And Necessary Conditions

In this paper, we study a periodic single-species logistic system with impulsive diffusion in two patches. By using the iterative method, sufficient and necessary conditions on the existence, uniqueness and global attractivity of positive periodic solution and the extinction of species for this system are established. Two examples and numerical simulations are presented to illustrate the feasibility of our results.

scholarly journals On Sufficient and Necessary Conditions in Bounded CTL: A Forgetting Approach

2020 ◽  
Author(s):  
Renyan Feng ◽  
Erman Acar ◽  
Stefan Schlobach ◽  
Yisong Wang ◽  
Wanwei Liu
Keyword(s):  
Computational Complexity ◽  
System Design ◽  
Formal Verification ◽  
Information Content ◽  
Necessary Conditions ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Computation Tree ◽  
Sufficient And Necessary Conditions ◽  
Points Of View

Computation Tree Logic (CTL) is one of the central formalisms in formal verification. As a specification language, it is used to express a property that the system at hand is expected to satisfy. From both the verification and the system design points of view, some information content of such property might become irrelevant for the system due to various reasons, e.g., it might become obsolete by time, or perhaps infeasible due to practical difficulties. Then, the problem arises on how to subtract such piece of information without altering the relevant system behaviour or violating the existing specifications over a given signature. Moreover, in such a scenario, two crucial notions are informative: the strongest necessary condition (SNC) and the weakest sufficient condition (WSC) of a given property. To address such a scenario in a principled way, we introduce a forgetting-based approach in CTL and show that it can be used to compute SNC and WSC of a property under a given model and over a given signature. We study its theoretical properties and also show that our notion of forgetting satisfies existing essential postulates of knowledge forgetting. Furthermore, we analyse the computational complexity of some basic reasoning tasks for the fragment CTLAF in particular.

scholarly journals Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1323
Author(s):  
Shyam Sundar Santra ◽  
Rami Ahmad El-Nabulsi ◽  
Khaled Mohamed Khedher
Keyword(s):  
Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Multiple Delays ◽  
Mixed Delays ◽  
Neutral Differential Equations ◽  
Canonical Operator ◽  
Second Order Differential Equations ◽  
The Future ◽  
Sufficient And Necessary Conditions

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study.

scholarly journals Properties of Certain Subclass of Meromorphic Multivalent Functions Associated with q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1035
Author(s):  
Cai-Mei Yan ◽  
Rekha Srivastava ◽  
Jin-Lin Liu
Keyword(s):  
Difference Operator ◽  
Necessary Conditions ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Closure Theorems ◽  
Sufficient And Necessary Conditions ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

A new subclass Σp,q(α,A,B) of meromorphic multivalent functions is defined by means of a q-difference operator. Some properties of the functions in this new subclass, such as sufficient and necessary conditions, coefficient estimates, growth and distortion theorems, radius of starlikeness and convexity, partial sums and closure theorems, are investigated.

scholarly journals Noetherian properties in composite generalized power series rings

2020 ◽  
Vol 18 (1) ◽  
pp. 1540-1551
Author(s):  
Jung Wook Lim ◽  
Dong Yeol Oh
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Commutative Rings ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Generalized Power Series ◽  
Ordered Monoid ◽  
Power Series Rings ◽  
Necessary And Sufficient ◽  
Equivalent Conditions

Abstract Let ({\mathrm{\Gamma}},\le ) be a strictly ordered monoid, and let {{\mathrm{\Gamma}}}^{\ast }\left={\mathrm{\Gamma}}\backslash \{0\} . Let D\subseteq E be an extension of commutative rings with identity, and let I be a nonzero proper ideal of D. Set \begin{array}{l}D+[\kern-2pt[ {E}^{{{\mathrm{\Gamma}}}^{\ast },\le }]\kern-2pt] := \left\{f\in [\kern-2pt[ {E}^{{\mathrm{\Gamma}},\le }]\kern-2pt] \hspace{0.15em}|\hspace{0.2em}f(0)\in D\right\}\hspace{.5em}\text{and}\\ \hspace{0.2em}D+[\kern-2pt[ {I}^{{\Gamma }^{\ast },\le }]\kern-2pt] := \left\{f\in [\kern-2pt[ {D}^{{\mathrm{\Gamma}},\le }]\kern-2pt] \hspace{0.15em}|\hspace{0.2em}f(\alpha )\in I,\hspace{.5em}\text{for}\hspace{.25em}\text{all}\hspace{.5em}\alpha \in {{\mathrm{\Gamma}}}^{\ast }\right\}.\end{array} In this paper, we give necessary conditions for the rings D+[\kern-2pt[ {E}^{{{\mathrm{\Gamma}}}^{\ast },\le }]\kern-2pt] to be Noetherian when ({\mathrm{\Gamma}},\le ) is positively ordered, and sufficient conditions for the rings D+[\kern-2pt[ {E}^{{{\mathrm{\Gamma}}}^{\ast },\le }]\kern-2pt] to be Noetherian when ({\mathrm{\Gamma}},\le ) is positively totally ordered. Moreover, we give a necessary and sufficient condition for the ring D+[\kern-2pt[ {I}^{{\Gamma }^{\ast },\le }]\kern-2pt] to be Noetherian when ({\mathrm{\Gamma}},\le ) is positively totally ordered. As corollaries, we give equivalent conditions for the rings D+({X}_{1},\ldots ,{X}_{n})E{[}{X}_{1},\ldots ,{X}_{n}] and D+({X}_{1},\ldots ,{X}_{n})I{[}{X}_{1},\ldots ,{X}_{n}] to be Noetherian.

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