scholarly journals Complicated dynamics of tumor-immune system interaction model with distributed time delay

2020 ◽  
Vol 25 (7) ◽  
pp. 2391-2406
Author(s):  
Min Yu ◽  
◽  
Gang Huang ◽  
Yueping Dong ◽  
Yasuhiro Takeuchi ◽  
...  
Keyword(s):  
Immune System ◽  
Time Delay ◽  
Interaction Model ◽  
Distributed Time Delay

Comparison of two different types of fractional-order COVID-19 distributed time-delay models with real data application

2021 ◽  
pp. 2150219
Author(s):  
Liangli Yang ◽  
Yongmei Su ◽  
Xinjian Zhuo
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Distributed Delay ◽  
Real Data ◽  
Least Square ◽  
Order Model ◽  
The Real ◽  
Fractional Order Model ◽  
Different Types ◽  
Distributed Time Delay

The outbreak of COVID-19 has a great impact on the world. Considering that there are different infection delays among different populations, which can be expressed as distributed delay, and the distributed time-delay is rarely used in fractional-order model to simulate the real data, here we establish two different types of fractional order (Caputo and Caputo–Fabrizio) COVID-19 models with distributed time-delay. Parameters are estimated by the least-square method according to the report data of China and other 12 countries. The results of Caputo and Caputo–Fabrizio model with distributed time-delay and without delay, the integer-order model with distributed delay are compared. These show that the fractional-order model can be better in fitting the real data. Moreover, Caputo order is better in short-term time fitting, Caputo–Fabrizio order is better in long-term fitting and prediction. Finally, the influence of several parameters is simulated in Caputo order model, which further verifies the importance of taking strict quarantine measures and paying close attention to the incubation period population.

Effect of Spray-Wall Interaction On Thermoacoustic Instability Prediction by Flame Transfer Function and the Convective Time Delay Method

2021 ◽  
Author(s):  
Sheng Meng ◽  
Man Zhang
Keyword(s):  
Time Delay ◽  
Transfer Function ◽  
Numerical Models ◽  
Time Lag ◽  
Interaction Model ◽  
Phase Lag ◽  
Thermoacoustic Instability ◽  
Spray Flame ◽  
Wall Interaction ◽  
Definition Of

Abstract This study numerically investigates the effect of spray-wall interactions on thermoacoustic instability prediction. The LES-based flame transfer function (FTF) and the convective time delay methods are used by combining the Helmholtz acoustic solver to predict a single spray flame under the so-called slip and film spray-wall conditions. It is found that considering more realistic film liquid and a wall surface interaction model achieves a more accurate phase lag in both of the time lag evaluations compared to the experimental results. Additionally, the results show that a new time delay exists between the liquid film fluctuation and the unsteady heat release, which explains the larger phase value in the film spray-wall condition than in the slip condition. Moreover, the prediction capability of the FTF framework and the convective time delay methodology in the linear regime are also presented. In general, the instability frequency differences predicted using the FTF framework under the film condition are less than 10 Hz compared with the experimental data. However, an underestimation of the numerical gain value leads to requiring a change in the forcing position and an improvement in the numerical models. Due to the ambiguous definition of the gain value in the convective time delay method, this approach leads to arbitrary and uncertain thermoacoustic instability predictions.

scholarly journals Minimal Wave Speed in a Predator-Prey System with Distributed Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Fuzhen Wu ◽  
Dongfeng Li
Keyword(s):  
Time Delay ◽  
Traveling Wave ◽  
Wave Speed ◽  
Upper And Lower Solutions ◽  
Traveling Wave Solutions ◽  
Predator Prey ◽  
Wave Solutions ◽  
Prey System ◽  
Minimal Wave Speed ◽  
Distributed Time Delay

This paper is concerned with the minimal wave speed of traveling wave solutions in a predator-prey system with distributed time delay, which does not satisfy comparison principle due to delayed intraspecific terms. By constructing upper and lower solutions, we obtain the existence of traveling wave solutions when the wave speed is the minimal wave speed. Our results complete the known conclusions and show the precisely asymptotic behavior of traveling wave solutions.

scholarly journals Overlapping Decentralized Controller Design for Descriptor-type Systems with Distributed Time-delay

2021 ◽  
Vol 20 ◽  
pp. 257-263
Author(s):  
Altug Iftar
Keyword(s):  
Time Delay ◽  
Large Scale ◽  
Controller Design ◽  
Original System ◽  
Type Systems ◽  
Large Scale System ◽  
Decentralized Controllers ◽  
Distributed Time Delay

Decentralized controller design using overlapping decompositions is considered for descriptor-type systems with distributed time-delay. The approach is based on the principle of extension. In this approach, a given large-scale system is decomposed overlappingly into a number of subsystems and expanded such that the overlapping parts appear as disjoint. A decentralized controller is then designed for the expanded system. This controller is then contracted for implementation on the original system. It is shown that if the decentralized controllers are designed to stabilize the expanded system and to achieve certain performance, then the contracted controller, which would have an overlapping decentralized structure, will stabilize the original system and will achieve corresponding performance

scholarly journals Controller Design for Descriptor-type Systems with Distributed Timedelay Using Extension

2021 ◽  
Vol 20 ◽  
pp. 27-32
Author(s):  
Altug Iftar
Keyword(s):  
Time Delay ◽  
Controller Design ◽  
Original System ◽  
Type Systems ◽  
Distributed Time Delay

Controller design using extension is considered for descriptor-type systems with distributed time-delay. The approach is useful in decentralized controller design using overlapping decompositions. In this approach, a given largescale system is decomposed overlappingly into a number of subsystems and expanded such that the overlapping parts appear as disjoint. Since the subsystems appear as disjoint for the expanded system, it is easier to design a descentralized controller for the expanded system. This controller is then contracted for implementation on the original system. In the present paper, it is shown how to contract such a controller to guarantee stability and desired performance for the original system

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