A Petri Net Approach to Persistence Analysis in Chemical Reaction Networks
نویسندگان
چکیده
A positive dynamical system is said to be persistent if every solution that starts in the interior of the positive orthant does not approach the boundary of this orthant. For chemical reaction networks and other models in biology, persistence represents a non-extinction property: if every species is present at the start of the reaction, then no species will tend to be eliminated in the course of the reaction. This paper provides checkable necessary as well as sufficient conditions for persistence of chemical species in reaction networks, and the applicability of these conditions is illustrated on some examples of relatively high dimension which arise in molecular biology. More specific results are also provided for reactions endowed with mass-action kinetics. Overall, the results exploit concepts and tools from Petri net theory as well as ergodic and recurrence theory.
منابع مشابه
A Petri net approach to the study of persistence in chemical reaction networks.
Persistence is the property, for differential equations in R(n), that solutions starting in the positive orthant do not approach the boundary of the orthant. For chemical reactions and population models, this translates into the non-extinction property: provided that every species is present at the start of the reaction, no species will tend to be eliminated in the course of the reaction. This ...
متن کاملFormal approach on modeling and predicting of software system security: Stochastic petri net
To evaluate and predict component-based software security, a two-dimensional model of software security is proposed by Stochastic Petri Net in this paper. In this approach, the software security is modeled by graphical presentation ability of Petri nets, and the quantitative prediction is provided by the evaluation capability of Stochastic Petri Net and the computing power of Markov chain. Each...
متن کاملA rule-based evaluation of ladder logic diagram and timed petri nets for programmable logic controllers
This paper describes an evaluation through a case study by measuring a rule-based approach, which proposed for ladder logic diagrams and Petri nets. In the beginning, programmable logic controllers were widely designed by ladder logic diagrams. When complexity and functionality of manufacturing systems increases, developing their software is becoming more difficult. Thus, Petri nets as a high l...
متن کاملModeling and Performance Evaluation of Energy Consumption in S-MAC Protocol Using Generalized Stochastic Petri Nets
One of the features of wireless sensor networks is that the nodes in this network have limited power sources. Therefore, assessment of energy consumption in these networks is very important. What has been common practice has been the use of traditional simulators to evaluate the energy consumption of the nodes in these networks. Simulators often have problems such as fluctuating output values i...
متن کاملTime Management Approach on a Discrete Event Manufacturing System Modeled by Petri Net
Discrete event system, Supervisory control, Petri Net, Constraint This paper presents a method to manage the time in a manufacturing system for obtaining an optimized model. The system in this paper is modeled by the timed Petri net and the optimization is performed based on the structural properties of Petri nets. In a system there are some states which are called forbidden states an...
متن کامل