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Analyzing Oscillatory Behavior with Formal Methods

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8453)

Abstract

An important behavioral pattern that can be witnessed in many systems is periodic re-occurrence. For example, most living organisms that we know are governed by a 24 hours rhythm that determines whether they are awake or not. On a larger scale, also whole population numbers of organisms fluctuate in a cyclic manner as in predator-prey relationships. When treating such systems in a deterministic way, i.e., assuming that stochastic effects are negligible, the analysis is a well-studied topic. But if those effects play an important role, recent publications suggest that at least a part of the system should be modeled stochastically. However, in that case, one quickly realizes that characterizing and defining oscillatory behavior is not a straightforward task, which can be solved once and for all. Moreover, efficiently checking whether a given system oscillates or not and if so determining the amplitude of the fluctuations and the time in-between is intricate. This paper shall give an overview of the existing literature on different modeling formalisms for oscillatory systems, definitions of oscillatory behavior, and the respective analysis methods.

Keywords

  • Model Check
  • Formal Method
  • Circadian Clock
  • Deterministic Model
  • Oscillatory Behavior

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Andreychenko, A., Krüger, T., Spieler, D. (2014). Analyzing Oscillatory Behavior with Formal Methods. In: Remke, A., Stoelinga, M. (eds) Stochastic Model Checking. Rigorous Dependability Analysis Using Model Checking Techniques for Stochastic Systems. ROCKS 2012. Lecture Notes in Computer Science, vol 8453. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45489-3_1

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