scholarly journals CONTINUOUS PETRI NETS: EXPRESSIVE POWER AND DECIDABILITY ISSUES

2010 ◽  
Vol 21 (02) ◽  
pp. 235-256 ◽  
Author(s):  
LAURA RECALDE ◽  
SERGE HADDAD ◽  
MANUEL SILVA
Keyword(s):  
Differential Equations ◽  
Petri Nets ◽  
Fundamental Problem ◽  
Discrete Event ◽  
Expressive Power ◽  
Timed Petri Nets ◽  
Analysis And Synthesis ◽  
Continuous Petri Nets ◽  
Linear Differential ◽  
The One

State explosion is a fundamental problem in the analysis and synthesis of discrete event systems. Continuous Petri nets can be seen as a relaxation of the corresponding discrete model. The expected gains are twofold: improvements in complexity and in decidability. In the case of autonomous nets we prove that liveness or deadlock-freeness remain decidable and can be checked more efficiently than in Petri nets. Then we introduce time in the model which now behaves as a dynamical system driven by differential equations and we study it w.r.t. expressiveness and decidability issues. On the one hand, we prove that this model is equivalent to timed differential Petri nets which are a slight extension of systems driven by linear differential equations (LDE). On the other hand, (contrary to the systems driven by LDEs) we show that continuous timed Petri nets are able to simulate Turing machines and thus that basic properties become undecidable.

scholarly journals Stability analysis and controller synthesis for hybrid dynamical systems

2010 ◽  
Vol 368 (1930) ◽  
pp. 4937-4960 ◽  
Author(s):  
W. P. M. H. Heemels ◽  
B. De Schutter ◽  
J. Lunze ◽  
M. Lazar
Keyword(s):  
Dynamical Systems ◽  
Mathematical Models ◽  
Hybrid Systems ◽  
Discrete Event ◽  
Research Area ◽  
Hybrid Dynamical Systems ◽  
Technological Systems ◽  
Analysis And Synthesis ◽  
Control Community ◽  
The One

Wherever continuous and discrete dynamics interact, hybrid systems arise. This is especially the case in many technological systems in which logic decision-making and embedded control actions are combined with continuous physical processes. Also for many mechanical, biological, electrical and economical systems the use of hybrid models is essential to adequately describe their behaviour. To capture the evolution of these systems, mathematical models are needed that combine in one way or another the dynamics of the continuous parts of the system with the dynamics of the logic and discrete parts. These mathematical models come in all kinds of variations, but basically consist of some form of differential or difference equations on the one hand and automata or other discrete-event models on the other hand. The collection of analysis and synthesis techniques based on these models forms the research area of hybrid systems theory, which plays an important role in the multi-disciplinary design of many technological systems that surround us. This paper presents an overview from the perspective of the control community on modelling, analysis and control design for hybrid dynamical systems and surveys the major research lines in this appealing and lively research area.

Petri Nets and Discrete Events Systems

2013 ◽  
pp. 231-240 ◽  
Author(s):  
Juan L. G. Guirao ◽  
Fernando L. Pelayo
Keyword(s):  
Dynamical Systems ◽  
Petri Nets ◽  
Discrete Event Systems ◽  
Discrete Event ◽  
Discrete Dynamical Systems ◽  
Discrete Events ◽  
Key Factors ◽  
Discrete Events Systems ◽  
The One ◽  
The Relationship

This paper provides an overview over the relationship between Petri Nets and Discrete Event Systems as they have been proved as key factors in the cognitive processes of perception and memorization. In this sense, different aspects of encoding Petri Nets as Discrete Dynamical Systems that try to advance not only in the problem of reachability but also in the one of describing the periodicity of markings and their similarity, are revised. It is also provided a metric for the case of Non-bounded Petri Nets.

Petri Nets and Discrete Events Systems

2011 ◽  
Vol 3 (3) ◽  
pp. 13-22
Author(s):  
Juan L. G. Guirao ◽  
Fernando L. Pelayo
Keyword(s):  
Petri Nets ◽  
Cognitive Processes ◽  
Discrete Event Systems ◽  
Discrete Event ◽  
Discrete Dynamical Systems ◽  
Discrete Events ◽  
Key Factors ◽  
Discrete Events Systems ◽  
The One ◽  
The Relationship

This paper provides an overview over the relationship between Petri Nets and Discrete Event Systems as they have been proved as key factors in the cognitive processes of perception and memorization. In this sense, different aspects of encoding Petri Nets as Discrete Dynamical Systems that try to advance not only in the problem of reachability but also in the one of describing the periodicity of markings and their similarity, are revised. It is also provided a metric for the case of Non-bounded Petri Nets.

scholarly journals New Symmetries of Black-Scholes Equation

2021 ◽  
Vol 20 ◽  
pp. 76-87
Author(s):  
Tshidiso Masebe
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Lie Point Symmetries ◽  
Invariant Solutions ◽  
One Dimensional ◽  
Black Scholes ◽  
Linear Differential ◽  
The One ◽  
Ordinary Linear Differential Equations

Lie Point symmetries and Euler’s formula for solving second order ordinary linear differential equations are used to determine symmetries for the one-dimensional Black- Scholes equation. One symmetry is utilized to determine an invariant solutions

scholarly journals Growth of solutions of second order complex linear differential equations with entire coefficients

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 275-284 ◽  
Author(s):  
Jianren Long
Keyword(s):  
Entire Function ◽  
Differential Equations ◽  
Nontrivial Solution ◽  
Infinite Order ◽  
Entire Functions ◽  
Order Complex ◽  
Complex Linear ◽  
Linear Differential ◽  
The One ◽  
Growth Of Solutions

Some new conditions on the entire coefficients A(z) and B(z), which guarantee every nontrivial solution of f''+A(z) f'+B(z) f = 0 is of infinite order, are given in this paper. Two classes of entire functions are involved in these conditions, the one is entire functions having Fabry gaps, the another is function extremal for Yang?s inequality. Moreover, a kind of entire function having finite Borel exception value is considered.

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