Introduction to Dynamic Systems and Stochastic Processes

Author(s):  
Jean-Pierre Signoret ◽  
Alain Leroy
Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 896
Author(s):  
Jan Awrejcewicz ◽  
José A. Tenreiro Machado

In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor and control complicated chaotic and stochastic processes [...]


Author(s):  
Zhonglai Wang ◽  
Zissimos P. Mourelatos ◽  
Jing Li ◽  
Amandeep Singh ◽  
Igor Baseski

Time-dependent reliability is the probability that a system will perform its intended function successfully for a specified time. Unless many and often unrealistic assumptions are made, the accuracy and efficiency of time-dependent reliability estimation are major issues which may limit its practicality. Monte Carlo simulation (MCS) is accurate and easy to use but it is computationally prohibitive for high dimensional, long duration, time-dependent (dynamic) systems with a low failure probability. This work addresses systems with random parameters excited by stochastic processes. Their response is calculated by time integrating a set of differential equations at discrete times. The limit state functions are therefore, explicit in time and depend on time-invariant random variables and time-dependent stochastic processes. We present an improved subset simulation with splitting approach by partitioning the original high dimensional random process into a series of correlated, short duration, low dimensional random processes. Subset simulation reduces the computational cost by introducing appropriate intermediate failure sub-domains to express the low failure probability as a product of larger conditional failure probabilities. Splitting is an efficient sampling method to estimate the conditional probabilities. The proposed subset simulation with splitting not only estimates the time-dependent probability of failure at a given time but also estimates the cumulative distribution function up to that time with approximately the same cost. A vibration example involving a vehicle on a stochastic road demonstrates the advantages of the proposed approach.


Author(s):  
Jonathan Bendor ◽  
Daniel Diermeier ◽  
David A. Siegel ◽  
Michael M. Ting

This chapter summarizes the book’s major findings regarding party location, turnout, voter choice, and voter participation. First, the simple party competition model suggests that in unidimensional policy spaces, satisficing by winners plus search by losers produces a string of governmental policies that converges to the median voter’s ideal point when citizens always vote for the party that will better serve their interests. Second, turnout responds in intuitive ways to changes in parameter values. Average participation is higher the further apart the parties, in both two-component models with fixed platforms and in the simple turnout model. Third, voters learn to support parties that better serve their interests. Fourth, voter coordination is usually successful: the Condorcet loser is almost never selected. The behavioral theory of elections based on bounded rationality is formulated in the languages of dynamic systems and stochastic processes.


2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Zhonglai Wang ◽  
Zissimos P. Mourelatos ◽  
Jing Li ◽  
Igor Baseski ◽  
Amandeep Singh

Time-dependent reliability is the probability that a system will perform its intended function successfully for a specified time. Unless many and often unrealistic assumptions are made, the accuracy and efficiency of time-dependent reliability estimation are major issues which may limit its practicality. Monte Carlo simulation (MCS) is accurate and easy to use, but it is computationally prohibitive for high dimensional, long duration, time-dependent (dynamic) systems with a low failure probability. This work is relevant to systems with random parameters excited by stochastic processes. Their response is calculated by time integrating a set of differential equations at discrete times. The limit state functions are, therefore, explicit in time and depend on time-invariant random variables and time-dependent stochastic processes. We present an improved subset simulation with splitting approach by partitioning the original high dimensional random process into a series of correlated, short duration, low dimensional random processes. Subset simulation reduces the computational cost by introducing appropriate intermediate failure sub-domains to express the low failure probability as a product of larger conditional failure probabilities. Splitting is an efficient sampling method to estimate the conditional probabilities. The proposed subset simulation with splitting not only estimates the time-dependent probability of failure at a given time but also estimates the cumulative distribution function up to that time with approximately the same cost. A vibration example involving a vehicle on a stochastic road demonstrates the advantages of the proposed approach.


Author(s):  
E. Naranjo

Equilibrium vesicles, those which are the stable form of aggregation and form spontaneously on mixing surfactant with water, have never been demonstrated in single component bilayers and only rarely in lipid or surfactant mixtures. Designing a simple and general method for producing spontaneous and stable vesicles depends on a better understanding of the thermodynamics of aggregation, the interplay of intermolecular forces in surfactants, and an efficient way of doing structural characterization in dynamic systems.


2010 ◽  
Vol 19 (3) ◽  
pp. 68-74 ◽  
Author(s):  
Catherine S. Shaker

Current research on feeding outcomes after discharge from the neonatal intensive care unit (NICU) suggests a need to critically look at the early underpinnings of persistent feeding problems in extremely preterm infants. Concepts of dynamic systems theory and sensitive care-giving are used to describe the specialized needs of this fragile population related to the emergence of safe and successful feeding and swallowing. Focusing on the infant as a co-regulatory partner and embracing a framework of an infant-driven, versus volume-driven, feeding approach are highlighted as best supporting the preterm infant's developmental strivings and long-term well-being.


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