Multi-State Dependent Impulsive Control for Pest Management

According to the integrated pest management strategies, we propose a model for pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove the existence of order one periodic solution of such system, and further, the attractiveness of the order one periodic solution by sequence convergence rules and qualitative analysis. Numerical simulations are carried out to illustrate the feasibility of our main results. Our results show that our method used in this paper is more efficient and easier than the existing ones for proving the existence of order one periodic solution

Threshold Dynamics of a Stochastic Chemostat Model with Two Nutrients and One Microorganism

A new stochastic chemostat model with two substitutable nutrients and one microorganism is proposed and investigated. Firstly, for the corresponding deterministic model, the threshold for extinction and permanence of the microorganism is obtained by analyzing the stability of the equilibria. Then, for the stochastic model, the threshold of the stochastic chemostat for extinction and permanence of the microorganism is explored. Difference of the threshold of the deterministic model and the stochastic model shows that a large stochastic disturbance can affect the persistence of the microorganism and is harmful to the cultivation of the microorganism. To illustrate this phenomenon, we give some computer simulations with different intensity of stochastic noise disturbance

A stage-structured predator-prey si model with disease in the prey and impulsive effects

This paper aims to develop a high-dimensional SI model with stage structure for both the prey (pest) and the predator, and then to investigate the dynamics of it. The model can be used for the study of Integrated Pest Management (IPM) which is a combination of constant pulse releasing of animal enemies and diseased pests at two different fixed moments. Firstly, we use analytical techniques for impulsive delay differential equations to obtain the conditions for global attractivity of the ‘pest-free’ periodic solution and permanence of the population model. It shows that the conditions strongly depend on time delay, impulsive release of animal enemies and infective pests. Secondly, we present a pest management strategy in which the pest population is kept under the economic threshold level (ETL) when the pest population is permanent. Finally, numerical analysis is presented to illustrate our main conclusion

SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects

We first propose a new epidemic disease model governed by system of impulsive delay differential equations. Then, based on theories for impulsive delay differential equations, we skillfully solve the difficulty in analyzing the global dynamical behavior of the model with pulse vaccination and impulsive population input effects at two different periodic moments. We prove the existence and global attractivity of the “infection-free” periodic solution and also the permanence of the model. We then carry out numerical simulations to illustrate our theoretical results, showing us that time delay, pulse vaccination, and pulse population input can exert a significant influence on the dynamics of the system which confirms the availability of pulse vaccination strategy for the practical epidemic prevention. Moreover, it is worth pointing out that we obtained an epidemic control strategy for controlling the number of population input

Dynamical Analysis of a Pest Management Model with Saturated Growth Rate and State Dependent Impulsive Effects

A new pest management mathematical model with saturated growth is proposed. The integrated pest management (IPM) strategy by introducing two state dependent pulses into the model is considered. Firstly, we analyze singular points of the model qualitatively and get the condition for focus point. Secondly, by using geometry theory of impulsive differential equation, the existence and stability of periodic solution of the system are discussed. Lastly, some examples and numerical simulations are given to illustrate our results

Threshold Dynamics of a Stochastic S

A stochastic SIR model with vertical transmission and vaccination is proposed and investigated in this paper. The threshold dynamics are explored when the noise is small. The conditions for the extinction or persistence of infectious diseases are deduced. Our results show that large noise can lead to the extinction of infectious diseases which is conducive to epidemic diseases control

Entwicklung eines Prüfstandes zur Langzeitmessung von seriell elastischen Stringaktoren

Um die Beweglichkeit des menschlichen Kniegelenks zu unterstützen, wird ein Stringaktor eingesetzt. Die Schnüre des Stringaktors sind die Hauptbestandsteile, deswegen liegt der Fokus dieser Arbeit vor allen auf der Schnurlebensdauer. In dieser Masterarbeit wird ein Prüfstand zur Lebensdauermessung der Schnüre konstruiert und aufgebaut. In der Ausarbeitung wird die Untersuchung der passenden Prüfmaterialien, die Konzeption und Konstruktion des Prüfstands und die Auslegung eines Testprotokolls zur Lebensdauermessung beschrieben. Im Rahmen dieser Arbeit werden zuerst die Anforderungen zur Auswahl der Prüfmaterialien generiert, die Tragfähigkeit und der Durchmesser der Schnüre werden bei der Auswahl der Prüfmaterialien fokussiert. Zum Thema Konzeption und Konstruktion des Prüfstands werden zuerst seine Funktionen definiert. Eine passende technische Lösung zum gesamten Prüfstand wird in unteren Abbildung gezeigt. Die Schnüre werden durch die Verdrehung des Motors des Stringantriebs verdrillt, daher verkürzen sich die Schnüre und erzeugen eine axiale Antriebskraft, welche dem Lastmoment des Motors Lastantriebs entgegenwirkt. Ein Faulhaber BLDC-Motor Serie 4490H024B wird für den Stringantriebs eingesetzt und um Lastmomente zu erzeugen wird ein Faulhaber DC-Motor Serie 3272H024V verwendet. Der Prüfstand wird nach der Auslegung und Konstruktion aller Bestandsteile zusammengebaut. Zur Automatisierung des Prüfstands wird zuerst die Beziehung zwischen Ausgangssignalen (Verdrehwinkel und Drehmoment der beiden Motoren) und Eingangssignale (Spannung und Strom der Netzteile) herausgefunden. Ein Ablaufdiagramm wurde für die Messung der Schnurlebensdauer in dieser Arbeit erstellt. Die Schnüre werden zwischen dem Motor des Stringantriebs und dem Läufer befestigt, durch den Lastmoment werden die Schnüre verspannt. Die Schnüre werden mit einer Lineargeschwindigkeit von 100 mm/s um 100 mm verkürzt, und dann wieder zur ursprünglichen Länge ausgedehnt. Die Zykluszahlen bzw. die Lebensdauer, welche die Schnüre durch solch Bewegungen erledigen muss bevor ein Versagen auftaucht, werden dokumentiert. Als Ausblick der Arbeit wird erwartet, dass mehrere Schnurmaterialien zu bestellen und ihre Lebensdauer zu messen sind, um ein Programm zur Motoransteuerung zu schreiben damit der Prüfstand automatisch laufen kann

Feedback Control of a Chaotic Finance System with Two Delays

In this research, we use the double-delayed feedback control (DDFC) method in order to control chaos in a finance system. Taking delays as parameters, the dynamic behavior of the system is investigated. Firstly, we study the local stability of equilibrium and the existence of local Hopf bifurcations. It can find that the delays can make chaos disappear and generate a stable equilibrium or periodic solution, which means the effectiveness of DDFC method. By using the normal form theory and center manifold argument, one derives the explicit algorithm for determining the properties of bifurcation. In addition, we also apply some mathematical methods (stability crossing curves) to show the stability changes of the financial system in two parameters’ τ1,τ2 plane. Finally, we give some numerical simulations by Matlab Microsoft to show the validity of theoretical analyses

Global Dynamics of a Predator–Prey Model with Fear Effect and Impulsive State Feedback Control

In this paper, a predator–prey model with fear effect and impulsive state control is proposed and analyzed. By constructing an appropriate Poincaré map, the dynamic properties of the system, including the existence, nonexistence, and stability of periodic solutions are studied. More specifically, based on the biological meaning, the pulse and the phase set are firstly defined in different regions as well as the corresponding Poincaré map. Subsequently, the properties of the Poincaré map are analyzed, and the existence of a periodic solution for the system is investigated according to the properties of the Poincaré map. We found that the existence of the periodic solution for the system completely depends on the property of the Poincaré map. Finally, several examples containing numerical simulations verify the obtained theoretical result

Chaos Control and Anticontrol of the Output Duopoly Competing Evolution Model

In the process of social development, there are a lot of competitions and confrontations. Participants in these competitions and confrontations always have different interests and goals. In order to achieve their goals, the participants must consider the opponent’s strategy to adjust their own strategies to achieve the interests of the optimization. This is called game. Based on the definition and its stability of the passive system, the passive control items are designed to the output of the duopoly competition evolution model, and the efficacy of the control methods is shown by the Lyapunov indexes. Then, the optimal function control method is taken to carry on the chaotic anticontrol to the chaotic system, and the Lyapunov indexes illustrate the control result. At last, the chaotic game of the system is introduced by combining the chaos control and anticontrol