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The present paper deals with the well-posedness and regularity of one class of one-dimensional time-dependent boundary-value problems with global boundary conditions on the entire time interval. We establish conditions for the well-posedness of boundary-value problems for partial differential equations in the class of bounded differentiable functions. A criterion for the regularity of the problem under consideration is also obtained. 相似文献
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LoSecco JM Bionta RM Biewitt G Bratton CB Casper D Chrysicopoulou P Claus R Cortez BG Errede S Foster GW Gajewski W Ganezer KS Goldhaber M Haines TJ Jones TW Kielczewska D Kropp WR Learned JG Lehmann E Park HS Reines F Schultz J Seidel S Shumard E Sinclair D Sobel HW Stone JL Sulak L Svoboda R van der Velde JC Wuest C 《Physical review letters》1985,54(21):2299-2301
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Nonlinear Dynamics - In this contribution, a modified oscillator of Tamasevicius et al. (Electron Lett 33:542–544, 1997) (referred to as the mTCMNL oscillator hereafter) is introduced with... 相似文献
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We perform a systematic analysis of a system consisting of a two-stage Colpitts oscillator. This well-known chaotic oscillator
is a modification of the standard Colpitts oscillator obtained by adding an extra transistor and a capacitor to the basic
circuit. The two-stage Colpitts oscillator exhibits better spectral characteristics compared to a classical single-stage Colpitts
oscillator. This interesting feature is suitable for chaos-based secure communication applications. We derive a smooth mathematical
model (i.e., sets of nonlinear ordinary differential equations) to describe the dynamics of the system. The stability of the
equilibrium states is carried out and conditions for the occurrence of Hopf bifurcations are obtained. The numerical exploration
reveals various bifurcation scenarios including period-doubling and interior crisis transitions to chaos. The connection between
the system parameters and various dynamical regimes is established with particular emphasis on the role of both bias (i.e.,
power supply) and damping on the dynamics of the oscillator. Such an approach is particularly interesting as the results obtained
are very useful for design engineers. The real physical implementation (i.e., use of electronic components) of the oscillator
is considered to validate the theoretical analysis through several comparisons between experimental and numerical results. 相似文献
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John?F?StinsEmail author G?Caroline?M?van Baal Tinca?JC?Polderman Frank?C?Verhulst Dorret?I?Boomsma 《BMC neuroscience》2004,5(1):49