By Valentin Afraimovich, José António Tenreiro Machado, Jiazhong Zhang
This ebook brings jointly 12 chapters on a brand new movement of study reading complicated phenomena in nonlinear systems—including engineering, physics, and social technological know-how. complicated Motions and Chaos in Nonlinear structures presents readers a specific vantage of the character and nonlinear phenomena in nonlinear dynamics that may enhance the corresponding mathematical thought and observe nonlinear layout to functional engineering in addition to the learn of alternative advanced phenomena together with these investigated inside social science.
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Additional info for Complex Motions and Chaos in Nonlinear Systems
Because of the strong influence of many uncontrollable random factors, experimenters are unable to create stable conditions for their reproducibility. Here we consider the approach defined earlier in [28, 29, 35] as the NAFASS and justify its application to a description of segments of various nonlinear signals having a multifrequency structure. t/ D A0 C K X ŒAk cos . k t/ C Bk sin . 35) kD1 This approach, proposed for the first time in [28, 29, 36], was based on some intuitive suppositions, but here we want to provide some additional arguments for its proper justification.
Y yD0 44 J. Zhang and Y. 6) All of these equations, the values are set at (0,0). 8) Nonlinear dynamics can be applied easily to the study of nonlinear phenomena governed by Eq. 8). 2 Boundary Layer Separation As boundary layer separation happens, the separation point is singular, and i the h hence @u D shear stress is null. 0;0/ 0, hence a1 D 0. 9) First, the stability of the flow separation point isÄ analyzed analytically. For the a2 a3 . Because a2 ¤ 0, equilibrium position (0,0), its Jacobean matrix is 0 12 a2 there are two nonzero eigenvalues, and they are real and different from each other, satisfying 1 C 2 D 12 a2 and 1 2 D 12 a22 .
X; y/ are functions of x and y. 4) where ai and bj are constants. The flows in the boundary near the wall satisfy the governing equations, and substituting Eq. 5) It is clear that bj can be expressed in terms of ai , and 7 of 16 parameters are independent. For clarity, make a1 , a2 , a3 , a4 , a5 , a7 , a8 independent parameters, and the shear stress, pressure, h iand their gradients are introduced to obtain their values. @u On the basis of D , we get a1 D . @y yD0 44 J. Zhang and Y. 6) All of these equations, the values are set at (0,0).