Silicon etch-refill p+-p-n+ epitaxial X-band IMPATT device

Glendinning, William B.; Mark, Andrew; Harmatz, M.

doi:10.1109/proc.1970.8048

Cited by 1 publication

(1 citation statement)

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“…Similarly additive white noise perturbations yield stochastic solutions that tend to Filippov's solution as ε → 0 [16,17]. Near singularities the situation can be more involved -discretizing near grazing points in the presence of a limit cycle leads to micro-chaos [18], and regularisations of two-fold singularities leads to a probabilistic notion of forward evolution [19,20]. In general, away from bifurcation points and determinacy-breaking singularities, the dynamics about a single discontinuity surface is robust to perturbations.…”

Section: Introductionmentioning

confidence: 99%

Jitter in Piecewise-Smooth Dynamical Systems with Intersecting Discontinuity Surfaces

Jeffrey¹,

Kafanas²,

Simpson

2018

Int. J. Bifurcation Chaos

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Mathematical models involving switches -in the form of differential equations with discontinuities -can accomodate real-world non-idealities through perturbations by hysteresis, time-delay, discretization, and noise. These are used to model the processes associated with switching in electronic control, mechanical contact, predator-prey preferences, and genetic or cellular regulation. The effect of such perturbations on rapid switching dynamics about a single switch are somewhat benign: in the limit that the size of the perturbation goes to zero the dynamics is given by Filippov's sliding solution. When multiple switches are involved, however, perturbations can have complicated effects, as shown in this paper. In the zero-perturbation limit, hysteresis, time-delay, and discretization cause erratic variation or 'jitter' for stable sliding motion, whilst noise generates a relatively regular sliding solution similar to the canopy solution (an extension of Filippov's solution to multiple switches). We illustrate the results with a model of a switched power circuit, and showcase a variety of complex phenomena that perturbations can generate, including chaotic dynamics, exit selection, and coexisting sliding solutions.

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Section: Introductionmentioning

confidence: 99%