scholarly journals Model of the nonlinear reaction system with autocatalysis and autoinhibition: Stability of dynamic states

2012 ◽  
Vol 66 (5) ◽  
pp. 637-646 ◽  
Author(s):  
Stevan Macesic ◽  
Zeljko Cupic ◽  
Ljiljana Kolar-Anic
Keyword(s):  
Sensitivity Analysis ◽  
Hopf Bifurcation ◽  
Network Analysis ◽  
Self Regulation ◽  
Reaction System ◽  
Model System ◽  
Economic Systems ◽  
Nonlinear Reaction ◽  
Stoichiometric Network Analysis ◽  
Theoretical Analyses

Self-regulation, achieved through positive (autocatalytic) or negative (autoinhibitory) feedback is commonly encountered in natural, technological and economic systems. The dynamic behavior of such systems is often complex and cannot be easily predicted, necessitating mathematical modelling and theoretical analyses. The aim of this work is to analyze the dynamics of a minimal model system with autocatalytic and autoinhibitory steps coupled through the same species, in order to understand under which critical condition the system loses stability and passes through an Andronov-Hopf bifurcation. The analysis used was improved stoichiometric network analysis (SNA) in combination with bifurcation and sensitivity analysis.

Constrained stoichiometric network analysis

2018 ◽  
Vol 20 (15) ◽  
pp. 9910-9921 ◽  
Author(s):  
Vuk Radojković ◽  
Igor Schreiber
Keyword(s):  
Hopf Bifurcation ◽  
Network Analysis ◽  
Linear Optimization ◽  
Reaction Network ◽  
Rate Coefficients ◽  
Bz Reaction ◽  
Stoichiometric Network Analysis

BZ reaction network – rate coefficients of reactions 11–14 were found by convex linear optimization at Hopf bifurcation.

scholarly journals Stoichiometric network analysis of a reaction system with conservation constraints

2018 ◽  
Vol 28 (8) ◽  
pp. 083114 ◽  
Author(s):  
Željko Čupić ◽  
Stevan Maćešić ◽  
Katarina Novakovic ◽  
Slobodan Anić ◽  
Ljiljana Kolar-Anić
Keyword(s):  
Network Analysis ◽  
Reaction System ◽  
Stoichiometric Network Analysis

scholarly journals Carcinogenesis and Chemotherapy Viewed from the Perspective of Stoichiometric Network Analysis (SNA): What Can the Biological System of the Elements Contribute to an Understanding of Tumour Induction by Elemental Chemical Noxae (e.g., Ni2+, Cd2+) and to an Understanding of Chemotherapy?

2003 ◽  
Vol 3 ◽  
pp. 319-341 ◽  
Author(s):  
Stefan Franzle ◽  
Bernd Markert
Keyword(s):  
Network Analysis ◽  
Biological System ◽  
Cell Biology ◽  
Essential Feature ◽  
Comprehensive Treatment ◽  
Biological Processes ◽  
Tumour Induction ◽  
Stoichiometric Network Analysis ◽  
Autocatalytic Networks

The biological application of stoichiometric network analysis (SNA) permits an understanding of tumour induction, carcinogenesis, and chemotherapy. Starting from the Biological System of the Elements, which provides a comprehensive treatment of the functions and distributions of chemical (trace) elements in biology, an attempt is made to interrelate the essential feature of biology and — regrettably — of tumour genesis by superimposing SNA reasoning on common features of all crucial biological processes. For this purpose, aspects, effects and drawbacks of autocatalysis (identical reproduction which can occur either under control or without control [in tumours]) are linked with the known facts about element distributions in living beings and about interference of metals with tumours (in terms of both chemotherapy and carcinogenesis). The essential role of autocatalysis in biology and the drawbacks of either controlled or spontaneous cell division can be used to understand crucial aspects of carcinogenesis and chemotherapy because SNA describes and predicts effects of autocatalysis, including phase effects that may be due to some kind of intervention. The SNA-based classifications of autocatalytic networks in cell biology are outlined here to identify new approaches to chemotherapy.

scholarly journals On the Network Analysis of the State Space of Discrete Dynamical Systems

2017 ◽  
Vol 27 (04) ◽  
pp. 1750062 ◽  
Author(s):  
Cheng Xu ◽  
Chengqing Li ◽  
Jinhu Lü ◽  
Shi Shu
Keyword(s):  
Dynamical Systems ◽  
Network Analysis ◽  
Cellular Automata ◽  
State Space ◽  
Discrete Dynamical Systems ◽  
The State ◽  
Dynamical Complexity ◽  
Two Parameters ◽  
Theoretical Analyses

This paper discusses the letter entitled “Network analysis of the state space of discrete dynamical systems” by A. Shreim et al. [Phys. Rev. Lett. 98, 198701 (2007)]. We found that some theoretical analyses are wrong and the proposed indicators based on two parameters of the state-mapping network cannot discriminate the dynamical complexity of the discrete dynamical systems composed of a 1D cellular automata.

Stability and Hopf Bifurcation of Nearest-Neighbor Coupled Neural Networks With Delays

2020 ◽  
Vol 15 (11) ◽  
Author(s):  
Lu Wang ◽  
Min Xiao ◽  
Shuai Zhou ◽  
Yurong Song ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Hopf Bifurcation ◽  
Nearest Neighbor ◽  
Multiple Delays ◽  
Dimensional System ◽  
Practical Applications ◽  
Coupled Neural Networks ◽  
The Stability ◽  
Related Characteristic ◽  
Theoretical Analyses

Abstract In this paper, a high-dimensional system of nearest-neighbor coupled neural networks with multiple delays is proposed. Nowadays, most present researches about neural networks have studied the connection between adjacent nodes. However, in practical applications, neural networks are extremely complicated. This paper further considers that there are still connection relationships between nonadjacent nodes, which reflect the intrinsic characteristics of neural networks more accurately because of the complexity of its topology. The influences of multiple delays on the local stability and Hopf bifurcation of the system are explored by selecting the sum of delays as bifurcation parameter and discussing the related characteristic equations. It is found that the dynamic behaviors of the system depend on the critical value of bifurcation. In addition, the conditions that ensure the stability of the system and the criteria of Hopf bifurcation are given. Finally, the correctness of the theoretical analyses is verified by numerical simulation.

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