Modeling of microbial growth bioprocesses — Equilibria and stability analysis

The paper addresses the analysis of nonlinear dynamical models of some microbial growth processes. Equilibrium points, stability analysis, and structural properties are studied for different bioprocesses with various kinetics structures. First, a simple micro-organism growth process on a single limiting substrate is widely analyzed. Second, a microbial growth process combined with an enzyme-catalyzed reaction is investigated. The analysis shows that these kinds of bioprocesses have multiple equilibria, stable or unstable, operational or non-operational. The partition of nonlinear model in linear and nonlinear parts via some structural properties leads to kinetic decoupling and facilitates the equilibria and stability analysis. The performed research is useful for model reduction and for the design of observers and control algorithms. To illustrate the study results, several numerical simulations are provided.

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Stability Analysis and Control of a New Smooth Chua's System

Abstract and Applied Analysis ◽

10.1155/2013/620286 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Guopeng Zhou ◽

Jinhua Huang ◽

Xiaoxin Liao ◽

Shijie Cheng

Keyword(s):

Stability Analysis ◽

Equilibrium Points ◽

Adaptive Controller ◽

Invariant Set ◽

Estimation Errors ◽

Linear Controller ◽

System A ◽

Chaotic Characteristic ◽

The Stability ◽

And Control

This paper is concerned with the stability analysis and control of a new smooth Chua's system. Firstly, the chaotic characteristic of the system is confirmed with the aid of the Lyapunov exponents. Secondly, it is proved that the system has globally exponential attractive set and positive invariant set. For the three unstable equilibrium points of the system, a linear controller is designed to globally exponentially stabilize the equilibrium points. Then, a linear controller and an adaptive controller are, respectively, proposed so that two similar types of smooth Chua's systems are globally synchronized, and the estimation errors of the uncertain parameters converge to zero asttends to infinity. Finally, the numerical simulations are also presented.

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Jacobi stability analysis of Rikitake system

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887816500985 ◽

2016 ◽

Vol 13 (07) ◽

pp. 1650098 ◽

Cited By ~ 13

Author(s):

M. K. Gupta ◽

C. K. Yadav

Keyword(s):

Dynamical System ◽

Differential Geometry ◽

Stability Analysis ◽

Nonlinear Differential Equations ◽

Equilibrium Points ◽

Nonlinear Dynamical System ◽

Intrinsic Properties ◽

Nonlinear Dynamical ◽

Rikitake System ◽

The Stability

We study the Rikitake system through the method of differential geometry, i.e. Kosambi–Cartan–Chern (KCC) theory for Jacobi stability analysis. For applying KCC theory we reformulate the Rikitake system as two second-order nonlinear differential equations. The five KCC invariants are obtained which express the intrinsic properties of nonlinear dynamical system. The deviation curvature tensor and its eigenvalues are obtained which determine the stability of the system. Jacobi stability of the equilibrium points is studied and obtain the conditions for stability. We study the dynamics of Rikitake system which shows the chaotic behaviour near the equilibrium points.

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Stability Analysis and Control Strategy for the Chained Propagation of Delay or Disruption Risk in a Port-Hinterland Service Network

Mathematical Problems in Engineering ◽

10.1155/2021/8859298 ◽

2021 ◽

Vol 2021 ◽

pp. 1-17

Author(s):

Haibo Kuang ◽

Pengfei Zhang ◽

Bing Han ◽

Peng Ouyang

Keyword(s):

Stability Analysis ◽

Control Strategy ◽

Recovery Rate ◽

Equilibrium Points ◽

External Factors ◽

Service Network ◽

Equilibrium Conditions ◽

Internal Factors ◽

Disruption Risk ◽

And Control

In a port-hinterland service network (PHSN), the occurrence of delays or disruption risks in the ports could impose serious impacts on carriers, nodes in hinterlands, or even the entire port-hinterland service network. To study how such risks are generated, propagated, and effectively controlled in the port-hinterland service network, this paper builds a model for the chained propagation of network risks that is consistent with the characteristics of the port-hinterland service network after analysing the risk factors and the risk-generating path by using the fuzzy analytic hierarchy process (FAHP) framework. On the premise of model stability analysis, the paper analyses the elasticity of carriers and ports to the infected proportion of nodes in the hinterlands, infection rate, and recovery rate in order to obtain the optimal control strategy and control coefficient, and the paper finally validates the model through a simulation analysis under a real case. The research shows that external factors causing delay or disruption risk are more important than internal factors, while the occurrence probability of external factors is lower than that of internal factors. There are four equilibrium points in this system. When the equilibrium conditions are met, the infected proportion of carriers and ports gradually approaches zero or narrows to a fixed ratio, and there is only one no-epidemic point. In the equilibrium conditions, when the infected proportion of inland ports is greater than a certain threshold, the infected proportion of carriers and ports decreases with an increase in the infected proportion of inland ports. Moreover, it is determined that increasing the recovery rate is the most effective and direct control measure. The results of this study provide new insights for the risk control of port-hinterland service network managers and participants.

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An Overview of the Stability Analysis of Recurrent Neural Networks With Multiple Equilibria

IEEE Transactions on Neural Networks and Learning Systems ◽

10.1109/tnnls.2021.3105519 ◽

2021 ◽

pp. 1-14

Author(s):

Peng Liu ◽

Jun Wang ◽

Zhigang Zeng

Keyword(s):

Neural Networks ◽

Stability Analysis ◽

Recurrent Neural Networks ◽

Multiple Equilibria ◽

The Stability

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Ayurveda Body–Mind Constitutional Types and Role of Yoga Intervention Among Type 2 Diabetes Mellitus Population of Chandigarh and Panchkula Regions

Annals of Neurosciences ◽

10.1177/09727531211000040 ◽

2021 ◽

pp. 097275312110000

Author(s):

Madhava Sai Sivapuram ◽

Vinod Srivastava ◽

Navneet Kaur ◽

Akshay Anand ◽

Raghuram Nagarathna ◽

...

Keyword(s):

Diabetes Mellitus ◽

Type 2 Diabetes ◽

Lipid Profiles ◽

Control Groups ◽

Yoga Intervention ◽

Positive Effects ◽

Study Results ◽

Significant Difference ◽

And Control

Background: Type 2 diabetes needs a better understanding of etiological factors and management strategies based on lifestyle and constitutional factors, given its high association rate with many cardiovascular, neurological disorders, and COVID-19 infection. Purpose: The present study was undertaken to investigate the effect of Diabetes-specific integrated Yoga lifestyle Protocol (DYP) on glycemic control and lipid profiles of diabetic adults. Along with the DYP intervention, the individuals residing in Chandigarh and Panchkula union territories in the northern part of India were assessed for Ayurveda-based body–mind constitutional type. Ayurveda describes body–mind constitution as “ prakriti,” which has been discussed from two angles, namely physiological and psychological as body and mind are correlated. Methods: Cluster sampling of waitlist control study subjects was used as the sampling method for the study. A total of 1,215 registered subjects (81 diabetic) responded in randomly selected clusters in Chandigarh and Panchkula. Ayurveda physicians did Ayurveda body–mind constitutional assessment called prakriti assessment (physiological body–mind constitution assessment) in 35 participants (23 diabetic, 12 prediabetic) as a part of the study. Results: A group of 50 subjects was randomly selected for yoga intervention out of 81 diabetes mellitus adults, and 31 subjects were enrolled as waitlist controls. A significant decrease in the glycosylated hemoglobin levels from 8.49 ± 1.94% to 7.97 ± 2.20% in the intervention group was noticed. The lipid profiles of the DYP intervention and control groups were monitored. Three-month follow-up results of lipid profile diagnostic tests in intervention and control groups showed a significant difference between the two groups ( P < 0.05). Most diabetic and prediabetic individuals were found to have pitta dosha ( pitta controls all heat, metabolism, and transformation in the mind and body) as dominant constitution type. Conclusion: The study results demonstrated significant positive effects of yoga in diabetic individuals. This study has indicated the evidence for the safety and efficacy of the validated DYP for community-level interventions to prevent maladies like brain damage and stroke.

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Dynamic Stability Analysis and Control of Power System Based on Nyquist Array Theory

2020 IEEE Power & Energy Society General Meeting (PESGM) ◽

10.1109/pesgm41954.2020.9281899 ◽

2020 ◽

Author(s):

Shiyun Xu ◽

Huadong Sun ◽

Shihui Fang ◽

Jingtian Bi ◽

Jun Yi ◽

...

Keyword(s):

Stability Analysis ◽

Power System ◽

Dynamic Stability ◽

And Control

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DIAPH2, PTPRD and HIC1 Gene Polymorphisms and Laryngeal Cancer Risk

International Journal of Environmental Research and Public Health ◽

10.3390/ijerph18147486 ◽

2021 ◽

Vol 18 (14) ◽

pp. 7486

Author(s):

Mirosław Śnit ◽

Maciej Misiołek ◽

Wojciech Ścierski ◽

Anna Koniewska ◽

Grażyna Stryjewska-Makuch ◽

...

Keyword(s):

Cancer Risk ◽

Laryngeal Cancer ◽

Basic Research ◽

Control Groups ◽

Allele Distribution ◽

Study Results ◽

Risk Patients ◽

And Control ◽

The Relationship

AIM, DIAPH2, PTPRD and HIC1 are the cell glycoprotein, which play an important role in the occurrence and development of tumors. This study was designed to assess the association between DIAPH2, PTPRD and HIC1 SNPs and laryngeal cancer risk. PATIENTS AND METHODS: This study including 267 patients with histologically confirmed laryngeal cancer and 157 controls. The relationship between genetic variations DIAPH2 (rs6620138), PTPRD (rs3765142) and HIC1 (rs9901806) and the onset of laryngeal cancer were investigated. Statistical analysis to calculate the relationship between DIAPH2, PTPRD and HIC1 genes polymorphism and pathogenesis of laryngeal cancer. RESULTS: The results showed that rs6620138 DIAPH2 polymorphism could increase the onset risk of laryngeal cancer. Statistically significant differences in allele distribution of rs6620138 DIAPH2 and rs9901806 HIC1 in the case and control groups subgroups. CONCLUSIONS: This study results suggested that genetic variation of rs6620138 DIAPH2 polymorphism is related to the susceptibility to laryngeal cancer. Our results provide a basis to begin basic research on the role of DIAPH2 gene in the pathogenesis of laryngeal cancer.

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