The analysis of cyclic stochastic fluid flows with time-varying transition rates

2015 ◽  
Vol 82 (1-2) ◽  
pp. 43-73 ◽  
Author(s):  
Barbara Margolius ◽  
Małgorzata M. O’Reilly
2016 ◽  
Author(s):  
William Gilpin ◽  
Vivek N. Prakash ◽  
Manu Prakash

1AbstractWe present a simple, intuitive algorithm for visualizing time-varying flow fields that can reveal complex flow structures with minimal user intervention. We apply this technique to a variety of biological systems, including the swimming currents of invertebrates and the collective motion of swarms of insects. We compare our results to more experimentally-diffcult and mathematically-sophisticated techniques for identifying patterns in fluid flows, and suggest that our tool represents an essential “middle ground” allowing experimentalists to easily determine whether a system exhibits interesting flow patterns and coherent structures without the need to resort to more intensive techniques. In addition to being informative, the visualizations generated by our tool are often striking and elegant, illustrating coherent structures directly from videos without the need for computational overlays. Our tool is available as fully-documented open-source code available for MATLAB, Python, or ImageJ at www.flowtrace.org.


Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Mengping Xing ◽  
Hao Shen ◽  
Zhen Wang

Based on the Lyapunov stability theory, this paper mainly investigates the H∞ synchronization problem for semi-Markovian jump neural networks (semi-MJNNs) with randomly occurring time-varying delays (TVDs). The continuous-time semi-MJNNs, where the transition rates are dependent on sojourn time, are introduced to make the issue under our consideration more general. One of the main characteristics of our work is the handling of TVDs. In addition to using the improved Jensen inequality and the reciprocal convexity lemma to deal with the integral inequality, we also employ Schur complement and the projection lemma to achieve the decoupling between the square term of TVDs. Finally, we verify the validity and feasibility of our method by a couple of simulation examples.


2013 ◽  
Vol 2013 ◽  
pp. 1-23
Author(s):  
Xinghua Liu ◽  
Hongsheng Xi

The exponential stability of neutral Markovian jump systems with interval mode-dependent time-varying delays, nonlinear perturbations, and partially known transition rates is investigated. A novel augmented stochastic Lyapunov functional is constructed, which employs the improved bounding technique and contains triple-integral terms to reduce conservativeness; then the delay-range-dependent and rate-dependent exponential stability criteria are developed by Lyapunov stability theory, reciprocally convex lemma, and free-weighting matrices. The corresponding results are extended to the uncertain case. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.


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