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The dynamics of a non‐linear discrete oscillator
Author(s) -
Wu Jingtang,
Yang Yongyi
Publication year - 1990
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490180105
Subject(s) - chaotic , simple (philosophy) , subspace topology , order (exchange) , mathematics , bifurcation , mathematical analysis , physics , statistical physics , nonlinear system , computer science , quantum mechanics , philosophy , epistemology , finance , artificial intelligence , economics
The dynamic behaviour of a simple second‐order discrete system with a single non‐linear factor, specified by ( x, y )‐ ( Ax + B ( y + sin(2π(x + y ))), x), (A, B) ϵ D = {(A, B): A, B ≥ 0, A + B < 1} ‐ is studied. the parameter subspace of D is analysed in detail. the bifurcation sets of the system are found. the existence of chaos in the system is proved by applying Marotto's theorem. the result of computer simulation agrees well with its analytical counterpart, and confirms that the single non‐linear factor ϕ = sin(2π( x + y )) is indeed the crucial point of a very complicated dynamic behaviour, including the alternative emergence of periodic, quasi‐periodic and chaotic phenomena, of this simple second‐order oscillator.