scholarly journals Modelling and Qualitative Analysis of Water Hyacinth Ecological System with Two State-Dependent Impulse Controls

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Jin-Bo Fu ◽  
Lan-Sun Chen
Keyword(s):  
Periodic Solution ◽  
Water Hyacinth ◽  
Existence Theorems ◽  
State Feedback Control ◽  
Ecological System ◽  
Indigenous Species ◽  
State Dependent ◽  
Negative Impacts ◽  
The Stability ◽  
Impulse Controls

Water hyacinth and its ecological invasion have negative impacts on diversity of indigenous species and ecosystems, which becomes one of the hotspots in current ecological research. In this paper, a water hyacinth ecological system with two state-dependent impulse controls is studied. Firstly, we define the successor functions of semicontinuous dynamic system and give existence theorems of order-1 periodic solution and order-2 periodic solution of such system. Secondly, we analyze singular points of the system without impulsive state feedback control qualitatively and get the condition for focus point. Thirdly, we obtain the sufficient condition under which the system has an order-1 or order-2 periodic solution through the method of successor function and prove the stability of the order-1 or order-2 periodic solution by the analogue of Poincaré’s criterion. Furthermore, some examples and numerical simulations are given to illustrate our results.

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.

scholarly journals The Study of a Predator-Prey Model with Fear Effect Based on State-Dependent Harvesting Strategy

Complexity ◽  
2022 ◽  
Vol 2022 ◽  
pp. 1-19
Author(s):  
Y. Tian ◽  
H. M. Li
Keyword(s):  
Numerical Simulation ◽  
Periodic Solution ◽  
Prey Population ◽  
Global Dynamics ◽  
Predator Population ◽  
Positive Order ◽  
Predator Prey ◽  
Predator Prey Model ◽  
State Dependent ◽  
The Stability

In presence of predator population, the prey population may significantly change their behavior. Fear for predator population enhances the survival probability of prey population, and it can greatly reduce the reproduction of prey population. In this study, we propose a predator-prey fishery model introducing the cost of fear into prey reproduction with Holling type-II functional response and prey-dependent harvesting and investigate the global dynamics of the proposed model. For the system without harvest, it is shown that the level of fear may alter the stability of the positive equilibrium, and an expression of fear critical level is characterized. For the harvest system, the existence of the semitrivial order-1 periodic solution and positive order- q ( q ≥ 1 ) periodic solution is discussed by the construction of a Poincaré map on the phase set, and the threshold conditions are given, which can not only transform state-dependent harvesting into a cycle one but also provide a possibility to determine the harvest frequency. In addition, to ensure a certain robustness of the adopted harvest policy, the threshold condition for the stability of the order- q periodic solution is given. Meanwhile, to achieve a good economic profit, an optimization problem is formulated and the optimum harvest level is obtained. Mathematical findings have been validated in numerical simulation by MATLAB. Different effects of different harvest levels and different fear levels have been demonstrated by depicting figures in numerical simulation using MATLAB.

scholarly journals Dynamics and bifurcation analysis of a state-dependent impulsive SIS model

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jinyan Wang
Keyword(s):  
Periodic Solution ◽  
Control Measures ◽  
Global Dynamics ◽  
Sis Model ◽  
Susceptible Population ◽  
Ode System ◽  
State Dependent ◽  
Existence And Stability ◽  
Modelling Studies ◽  
The Stability

AbstractRecently, considering the susceptible population size-guided implementations of control measures, several modelling studies investigated the global dynamics and bifurcation phenomena of the state-dependent impulsive SIR models. In this study, we propose a state-dependent impulsive model based on the SIS model. We firstly recall the complicated dynamics of the ODE system with saturated treatment. Based on the dynamics of the ODE system, we firstly discuss the existence and the stability of the semi-trivial periodic solution. Then, based on the definition of the Poincaré map and its properties, we systematically investigate the bifurcations near the semi-trivial periodic solution with all the key control parameters; consequently, we prove the existence and stability of the positive periodic solutions.

Dynamic analysis of conversion from a drug-sensitivity strain to a drug-resistant strain

2018 ◽  
Vol 11 (08) ◽  
pp. 1850113
Author(s):  
Zhong Zhao ◽  
Fengmei Tao ◽  
Qiuying Li
Keyword(s):  
Periodic Solution ◽  
Resistant Strain ◽  
Drug Sensitivity ◽  
Sufficient Conditions ◽  
Continuous System ◽  
State Feedback Control ◽  
Drug Resistant ◽  
Qualitative Properties ◽  
Optimal Criterion ◽  
The Stability

In this paper, a mathematical model of conversion from a drug-sensitivity strain to a drug-resistant strain is given to investigate how antibiotic usage may be optimized to preserve or restore antibiotic effectiveness. This novel theoretical framework could result in an optimal criterion on how to reduce the drug resistance to a reasonable range by using the antibiotic dressing strategy. The sufficient conditions of existence of order-1 periodic solution are obtained in view of the geometrical theory of the semi-continuous dynamical system and the qualitative properties of the corresponding continuous system. The stability of the order-1 periodic solution is proved by means of [H. J. Guo, L. S. Chen and X. Y. Song, Qualitative analysis of impulsive state feedback control to an algae-fish system with bistable property, Appl. Math. Comput. 271 (2015) 905–922]. Finally, our results are confirmed by means of numerical simulations.

Dynamical analysis of a two-species competitive system with state feedback impulsive control

2020 ◽  
Vol 13 (05) ◽  
pp. 2050007
Author(s):  
Jing Xu ◽  
Mingzhan Huang ◽  
Xinyu Song
Keyword(s):  
Periodic Solution ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Competitive System ◽  
Competitive Systems ◽  
State Dependent ◽  
Existence And Stability ◽  
The Stability ◽  
Theoretical Results

In this paper, three competitive systems with different kinds of state-dependent control are presented and investigated. The existence of the order-1 homoclinic orbit and order-1 periodic solution of the two systems that incorporate just one kind of state-dependent control is obtained by applying differential equation geometry theory, and the stability of the order-1 periodic solution of each system is also given. Besides, sufficient conditions for the existence and stability of the order-2 periodic solution of the system that incorporate two kinds of state-dependent control are gained by successor function method and analogue of Poincaré criterion, respectively. Finally, numerical simulations are carried out to verify the theoretical results.

Study of The Pharmacological Activity and Heavy Metal Content of Eichhornia Crassipes Extract

2019 ◽  
Vol 2 (2) ◽  
pp. 91-95 ◽  
Author(s):  
Jimmy Jimmy ◽  
Diah Indriani Widiputri ◽  
Paulus Gunawan
Keyword(s):  
Heavy Metal ◽  
Pharmacological Activity ◽  
Water Hyacinth ◽  
Metal Content ◽  
Eichhornia Crassipes ◽  
High Light Intensity ◽  
Milling Process ◽  
Heavy Metal Content ◽  
Solvent Ratio ◽  
Negative Impacts

Eichhornia crassipes is well-known as water hyacinth. Water hyacinth grows rapidly in the nutrient-rich water and high light intensity places. The uncontrollable growth of water hyacinth has caused many negative impacts to the environment. For instance, interrupted water transport and decreased population of aquatic lives. The capacity of utilising water hyacinth is slower than water hyacinth growth and water hyacinth is still considered as a threat to theecosystem. This work was focused on the study of the pharmacological activity and heavy metal content of water hyacinth in Lake Cipondoh, Tangerang. Fresh water hyacinth was pre-treated through oven-drying and milling process. After that, each part of the plant was macerated by using multiple extraction method with 96% ethanol/water and three variations of sample-to-solvent ratios (1:30, 1:50, and 1:75 w/v). The result of the experiment showed thatwater hyacinth leaves produced an extract with lowest IC 50 (55.76 ± 6.73 ppm) compared toother parts. The most optimum solvent used to achieve this result was 96% ethanol/water (1:1 v/v). In order to obtain the lowest antioxidant activity, the sample to solvent ratio used was 1:50 and the heavy metal in the extract was very low. With this result, it was concluded that there is a promising opportunity to apply the water hyacinth growing in Lake Cipondoh, Tangerang as herbal medicine ingredient. Through this utilization, the overall number of water hyacinth in Indonesia can be reduced or at the least be controlled, so that the environmental problem caused by this plant can be minimized.

Stabilization of networked switched affine systems with event-triggered strategy

2021 ◽  
pp. 014233122110213
Author(s):  
Dandan Li ◽  
Zhiqiang Zuo ◽  
Yijing Wang
Keyword(s):  
Affine Systems ◽  
Switching Law ◽  
Event Time ◽  
Sliding Motion ◽  
State Dependent ◽  
Event Triggering ◽  
Stability Issue ◽  
The Stability ◽  
Event Based ◽  
Selection Of

Using an event-based switching law, we address the stability issue for continuous-time switched affine systems in the network environment. The state-dependent switching law in terms of the region function is firstly developed. We combine the region function with the event-triggering mechanism to construct the switching law. This can provide more candidates for the selection of the next activated subsystem at each switching instant. As a result, it is possible for us to activate the appropriate subsystem to avoid the sliding motion. The Zeno behavior for the switched affine system can be naturally ruled out by guaranteeing a positive minimum inter-event time between two consecutive executions of the event-triggering threshold. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.

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