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15 February 2025 |
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Article overview
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Gradient and passive circuit structure in a class of non-linear dynamics on a graph | Herbert Mangesius
; Jean-Charles Delvenne
; Sanjoy K. Mitter
; | Date: |
2 Aug 2015 | Abstract: | We consider a class of non-linear dynamics on a graph with non-symmetric
weighting and provide a systematic method to formulate the governing ODE system
in gradient descent form of sum-separable strictly convex energy functions. By
that we establish a family of sum-separable Lyapunov functions for this class,
it coincides with Csisz’ar’s information divergences. Our approach bases on
structure results from passive network synthesis and on a transformation of the
original problem to a mass-preserving transport problem. We solve a conjecture
of P. Moylan related to the existence of a function inverse in the context of
realizing a non-linear ODE system as non-linear circuit. This work brings
together in novel ways Markov chain theory, circuit theory, and network
systems, in the framework of gradient flows on graphs. We discuss possible
applications in the context of coupled oscillator and electric power grid
studies and propose a discrete version of De Bruijn’s identity relating entropy
production to Fisher information. | Source: | arXiv, 1508.0237 | Services: | Forum | Review | PDF | Favorites |
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