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oapen-20.500.12657-850652023-11-15T09:17:26Z Weakly Nonlinear Systems Beffa, Federico Nonlinear Systems Weakly Nonlinear Systems Dynamical Systems Compley Systems Complexity bic Book Industry Communication::G Reference, information & interdisciplinary subjects::GP Research & information: general::GPF Information theory::GPFC Cybernetics & systems theory bic Book Industry Communication::T Technology, engineering, agriculture::TJ Electronics & communications engineering::TJK Communications engineering / telecommunications::TJKW WAP (wireless) technology bic Book Industry Communication::T Technology, engineering, agriculture::TJ Electronics & communications engineering::TJK Communications engineering / telecommunications The open access book covers a large class of nonlinear systems with many practical engineering applications. The approach is based on the extension of linear systems theory using the Volterra series. In contrast to the few existing treatments, our approach highlights the algebraic structure underlying such systems and is based on Schwartz’s distributions (rather than functions). The use of distributions leads naturally to the convolution algebras of linear time-invariant systems and the ones suitable for weakly nonlinear systems emerge as simple extensions to higher order distributions, without having to resort to ad hoc operators. The result is a much-simplified notation, free of multiple integrals, a conceptual simplification, and the ability to solve the associated nonlinear differential equations in a purely algebraic way. The representation based on distributions not only becomes manifestly power series alike, but it includes power series as the description of the subclass of memory-less, time-invariant, weakly nonlinear systems. With this connection, many results from the theory of power series can be extended to the larger class of weakly nonlinear systems with memory. As a specific application, the theory is specialised to weakly nonlinear electric networks. The authors show how they can be described by a set of linear equivalent circuits which can be manipulated in the usual way. The authors include many real-world examples that occur in the design of RF and mmW analogue integrated circuits for telecommunications. The examples show how the theory can elucidate many nonlinear phenomena and suggest solutions that an approach entirely based on numerical simulations can hardly suggest. The theory is extended to weakly nonlinear time-varying systems, and the authors show examples of how time-varying electric networks allow implementing functions unfeasible with time-invariant ones. The book is primarily intended for engineering students in upper semesters and in particular for electrical engineers. Practising engineers wanting to deepen their understanding of nonlinear systems should also find it useful. The book also serves as an introduction to distributions for undergraduate students of mathematics. 2023-11-13T16:42:07Z 2023-11-13T16:42:07Z 2024 book ONIX_20231113_9783031406812_22 9783031406812 9783031406805 https://library.oapen.org/handle/20.500.12657/85065 eng Understanding Complex Systems application/pdf n/a 978-3-031-40681-2.pdf https://link.springer.com/978-3-031-40681-2 Springer Nature Springer Nature Switzerland 10.1007/978-3-031-40681-2 10.1007/978-3-031-40681-2 6c6992af-b843-4f46-859c-f6e9998e40d5 1ca7d9ef-b641-4f72-8220-b5a3c6bfb19a 9783031406812 9783031406805 Springer Nature Switzerland 371 Cham [...] open access
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The open access book covers a large class of nonlinear systems with many practical engineering applications. The approach is based on the extension of linear systems theory using the Volterra series. In contrast to the few existing treatments, our approach highlights the algebraic structure underlying such systems and is based on Schwartz’s distributions (rather than functions). The use of distributions leads naturally to the convolution algebras of linear time-invariant systems and the ones suitable for weakly nonlinear systems emerge as simple extensions to higher order distributions, without having to resort to ad hoc operators. The result is a much-simplified notation, free of multiple integrals, a conceptual simplification, and the ability to solve the associated nonlinear differential equations in a purely algebraic way. The representation based on distributions not only becomes manifestly power series alike, but it includes power series as the description of the subclass of memory-less, time-invariant, weakly nonlinear systems. With this connection, many results from the theory of power series can be extended to the larger class of weakly nonlinear systems with memory. As a specific application, the theory is specialised to weakly nonlinear electric networks. The authors show how they can be described by a set of linear equivalent circuits which can be manipulated in the usual way. The authors include many real-world examples that occur in the design of RF and mmW analogue integrated circuits for telecommunications. The examples show how the theory can elucidate many nonlinear phenomena and suggest solutions that an approach entirely based on numerical simulations can hardly suggest. The theory is extended to weakly nonlinear time-varying systems, and the authors show examples of how time-varying electric networks allow implementing functions unfeasible with time-invariant ones. The book is primarily intended for engineering students in upper semesters and in particular for electrical engineers. Practising engineers wanting to deepen their understanding of nonlinear systems should also find it useful. The book also serves as an introduction to distributions for undergraduate students of mathematics.
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