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Our proofs are mainly based on continuation methods.
The asymptotic predictions are tested by comparison with numerical integrations of extinction curves based on continuation methods.
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Instead, formulations based on continuation along rays in parameter space are preferred.
The proof of existence theorem is based on the continuation method of Krasnosielski et al., Mawhin et al., and the Leray-Schauder degree.
The nonlinear equations of motion are studied by using (i) a code based on arclength continuation method that allows bifurcation analysis and (ii) direct time integration.
Moreover, using a code based on arclength continuation method, a bifurcation analysis is carried out for a special case with two-to-one internal resonance between the first and second doubly symmetric modes with respect to the panel's center (ω13≈2ω11).
Another interesting development is an approach based on continuations, a notion taken from programming language theory (where a continuation is a program execution state as determined by the steps still to be executed after the current instruction).
The numerical algorithm for this analysis is based on the parameter continuation methods and the "control parameter subspace changing".
Convenient matrix descriptions are used in order to facilitate the analysis based on Galerkin and continuation methods.
One of the earliest attempts is based on so-called continuation methods, such as simulated annealing [8] and the graduated non-convexity procedure [9].
Our proof is based on the homotopy continuation method together with a prior estimate.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com