Periodic response and crisis behavior for a system with piecewise-smooth non-linearities

1992 ◽  
Vol 27 (5) ◽  
pp. 833-843 ◽  
Author(s):  
Young B. Kim ◽  
Sherif T. Noah
Keyword(s):  
Piecewise Smooth ◽  
Periodic Response ◽  
Crisis Behavior

Brokering Peace in Nuclear Environments

2018 ◽  
Author(s):  
Moeed Yusuf
Keyword(s):  
Cold War ◽  
Third Party ◽  
Bargaining Theory ◽  
The Third ◽  
China And India ◽  
International Setting ◽  
Multiple Audiences ◽  
Crisis Behavior ◽  
The Cold War ◽  
Shed Light

This book is the first to theorize third party mediation in crises between regional nuclear powers. Its relevance flows from two of the most significant international developments since the end of the Cold War: the emergence of regional nuclear rivalries; and the shift from the Cold War’s bipolar context to today’s unipolar international setting. Moving away from the traditional bilateral deterrence models, the book conceptualizes crisis behavior as “brokered bargaining”: a three-way bargaining framework where the regional rivals and the ‘third party’ seek to influence each other to behave in line with their crisis objectives and in so doing, affect each other’s crisis behavior. The book tests brokered bargaining theory by examining U.S.-led crisis management in South Asia, analyzing three major crises between India and Pakistan: the Kargil conflict, 1999; the 2001-02 nuclear standoff; and the Mumbai crisis, 2008. The case studies find strong evidence of behavior predicted by the brokered bargaining framework. They also shed light on several risks of misperceptions and inadvertence due to the challenges inherent in signaling to multiple audiences simultaneously. Traditional explanations rooted in bilateral deterrence models do not account for these, leaving a void with serious practical consequences, which the introduction of brokered bargaining seeks to fill. The book’s findings also offer lessons for crises on the Korean peninsula, between China and India, and between potential nuclear rivals in the Middle East.

A Model for Addressing Crisis Behavior in Youth With Autism Spectrum Disorder Within a Functional and Contextual Framework

2020 ◽  
pp. 386-407
Author(s):  
Bryan H. King ◽  
Agnieszka Rynkiewicz ◽  
Małgorzata Janas-Kozik ◽  
Marta Tyszkiewicz-Nwafor
Keyword(s):  
Autism Spectrum Disorder ◽  
Behavior Management ◽  
Management Strategies ◽  
Autism Spectrum ◽  
Spectrum Disorder ◽  
Behavior Intervention Plan ◽  
Intervention Plan ◽  
Contextual Framework ◽  
Multiple Issues ◽  
Crisis Behavior

This chapter provides a model that extends the current resources available for crisis behavior assessment and intervention for youth with autism spectrum disorder (ASD) and co-occurring psychiatric conditions who are in crisis stabilization settings. Visual diagrams and intervention materials incorporated into this chapter illustrate the use of both preventative and responsive behavior management strategies that can be implemented in a time of crisis to stabilize and treat the psychiatric patient with ASD. The chapter begins with a review of a contextual method for evaluating and understanding the function of the presenting crisis behavior by considering the multiple issues that can underlie the crisis presentation. Working from this contextual model, the chapter then provides a blueprint for implementing intervention strategies to address crisis behaviors. This includes a table illustrating key elements to consider when developing a behavior intervention plan for dissemination and generalization.

scholarly journals Singularly Perturbed Oscillators with Exponential Nonlinearities

2021 ◽  
Author(s):  
S. Jelbart ◽  
K. U. Kristiansen ◽  
P. Szmolyan ◽  
M. Wechselberger
Keyword(s):  
Limit Cycles ◽  
Space Dimension ◽  
Blow Up ◽  
Exponential Convergence ◽  
Model System ◽  
Piecewise Smooth ◽  
Singularly Perturbed ◽  
Model Systems ◽  
Smooth System ◽  
Unique Limit

AbstractSingular exponential nonlinearities of the form $$e^{h(x)\epsilon ^{-1}}$$ e h ( x ) ϵ - 1 with $$\epsilon >0$$ ϵ > 0 small occur in many different applications. These terms have essential singularities for $$\epsilon =0$$ ϵ = 0 leading to very different behaviour depending on the sign of h. In this paper, we consider two prototypical singularly perturbed oscillators with such exponential nonlinearities. We apply a suitable normalization for both systems such that the $$\epsilon \rightarrow 0$$ ϵ → 0 limit is a piecewise smooth system. The convergence to this nonsmooth system is exponential due to the nonlinearities we study. By working on the two model systems we use a blow-up approach to demonstrate that this exponential convergence can be harmless in some cases while in other scenarios it can lead to further degeneracies. For our second model system, we deal with such degeneracies due to exponentially small terms by extending the space dimension, following the approach in Kristiansen (Nonlinearity 30(5): 2138–2184, 2017), and prove—for both systems—existence of (unique) limit cycles by perturbing away from singular cycles having desirable hyperbolicity properties.

scholarly journals The vibro-impact capsule system in millimetre scale: numerical optimisation and experimental verification

Meccanica ◽  
2020 ◽  
Vol 55 (10) ◽  
pp. 1885-1902
Author(s):  
Yang Liu ◽  
Joseph Páez Chávez ◽  
Jiajia Zhang ◽  
Jiyuan Tian ◽  
Bingyong Guo ◽  
...  
Keyword(s):  
Dynamical System ◽  
Mathematical Formulation ◽  
Path Following ◽  
Piecewise Smooth ◽  
Experimental Results ◽  
Scale Down ◽  
Speed Up ◽  
Small Bowel Endoscopy ◽  
Numerical Optimisation ◽  
Smooth Dynamical System

Abstract The vibro-impact capsule system has been studied extensively in the past decade because of its research challenges as a piecewise-smooth dynamical system and broad applications in engineering and healthcare technologies. This paper reports our team’s first attempt to scale down the prototype of the vibro-impact capsule to millimetre size, which is 26 mm in length and 11 mm in diameter, aiming for small-bowel endoscopy. Firstly, an existing mathematical model of the prototype and its mathematical formulation as a piecewise-smooth dynamical system are reviewed in order to carry out numerical optimisation for the prototype by means of path-following techniques. Our numerical analysis shows that the prototype can achieve a high progression speed up to 14.4 mm/s while avoiding the collision between the inner mass and the capsule which could lead to less propulsive force on the capsule so causing less discomfort on the patient. Secondly, the experimental rig and procedure for testing the prototype are introduced, and some preliminary experimental results are presented. Finally, experimental results are compared with the numerical results to validate the optimisation as well as the feasibility of the vibro-impact technique for the potential of a controllable endoscopic procedure.

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