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 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 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 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.

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.

scholarly journals VARIABILTY AND STABILTY OF TUBER YIELD OF JERUSALEM ARTICHOKE (Helianthus tuberosus L.) / VARIABILIDAD Y ESTABILIDAD DEL RENDIMIENTO DE TUBERCULOS DEL TOPINAMBO / VARIABILITÉ ET STABILITÉ DU RENDEMENT DU TUBERCULE DE TOPINAMBUR

Helia ◽  
2001 ◽  
Vol 24 (35) ◽  
pp. 25-32 ◽  
Author(s):  
Janoš Berenji ◽  
Vladimir Sikora
Keyword(s):  
Tuber Yield ◽  
Jerusalem Artichoke ◽  
Tuber Size ◽  
Yield Stability ◽  
Tuber Number ◽  
High Yield ◽  
Helianthus Tuberosus ◽  
Variety Trial ◽  
Stable Performance ◽  
The Stability

SUMMARYThe objective of this paper was to estimate the genetic and ecological variation as well as the stability of tuber yield per plant, tuber number per plant and tuber size of Jerusalem artichoke based on the results of a variety trial carried out with 20 different Jerusalem artichoke varieties during the period of 1994-2000. Significant genetic as well as ecologycal variation was observed for all of the traits studied. The most promissing varieties showing high tuber yield combined with high yield stability were “BT-4”, “Violet Rennes” and “UKR 4/ 82”. It is encouraging that the highest yielding varieties exibited a rather stable performance over environments.

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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