... to transform the nonlinear partial differential equations into nonlinear ordinary differential equations. The steady-state response, various bifurcations, and chaotic behavior of the system are studied by the multiple scales method and Runge–Kutta method. The dynamical characteristics of the system...

... of the equilibrium positions of the human-BB dynamical system. Similarly, ankle displacement in the upward direction with respect to the BB pivot also plays a critical role in the stability properties of the human-BB system. This paper investigates these effects through bifurcation analyses performed to the ankle...

... , … Fig. 3( a ) shows the asynchronous periodic oscillations with x i = − u i when σ 1 = 3 and σ 2 = 4 because the system undergoes a Hopf bifurcation for σ = σ 1 , 0 + . Figure 3( b ) illustrates that the trivial rest point...

...Shan Yin; Jinchen Ji; Shuning Deng; Guilin Wen Saddle-node or period-doubling bifurcations of the near-grazing impact periodic motions have been extensively studied in the impact oscillators, but the near-grazing Neimark-Sacker bifurcations have not been discussed yet. For the first time...

.... Editor: Firdaus Udwadia. 12 04 2018 20 07 2018 Bifurcations Chaotic dynamics Control Nonlinear dynamical systems Stability of nonlinear systems Networks synchronization has attracted a lot of attention in last years and one of the main reasons is that networks...

.... The rotating shaft is simulated by Timoshenko beam finite element with the consideration of geometric asymmetry. Applying the Lagrange's equations, the motion equations of the rotor-bearing-labyrinth seal system are derived. By means of spectrum cascades, bifurcation diagrams, Poincaré maps, etc...

... 2017 25 02 2018 Bifurcations Design optimization Nonlinear phenomena Perturbation Reduced-order models Dynamical analysis Dynamical method Asymptotic models Concurrent advances in precision manufacturing, material science, and computational design methods have produced...

... parameter, short bearing has large operating speed compared to a long bearing. The results are presented in the form of a bifurcation diagram and Poincaré map of the oscillations based on numerical computation. The considered unbalanced system shows periodic, multiperiodic, and quasi-periodic motion...

... in the below equation: (2) L d α f t d t α = s α L f t − ∑ k = 0 m − 1 s α − k − 1 f k 0 A detailed study of the FO bifurcation analyses of the proposed seven FOSs against the bifurcation parameter...

... ( 2 ), pp. 1151 – 1156 . 10.1007/s11071-013-1198-8 [16] Casini , P. , and Vestroni , F. , 2011 , “ Characterization of Bifurcating Non-Linear Normal Modes in Piecewise Linear Mechanical Systems ,” Int. J. Non-Linear Mech. , 46 ( 1 ), pp. 142 – 150 . 10.1016/j.ijnonlinmec.2010.08.002...

..., identified parameters of AMB model may contain the parametric uncertainty [ 14 ]. The combination of these nonlinearities and parametric uncertainty may cause significant influence on the vibration characteristics. Analytical solution systems Bifurcations Control Nonlinear dynamical systems...

... and branch structure in bifurcation diagrams to the system. The peak of postflutter response is also related to these parameters and the lower response peak can be obtained when the store mass center is in front of the elastic center. The models and results are helpful to the design procedure of the slender...

... Bifurcations Computational mechanics Flexible-cody dynamics Nonlinear dynamical systems Nonlinear oscillations Stability Structural dynamics Vibration Functionally graded (FG) materials [ 1 ] are the revolutionary class of inhomogeneous (or composite [ 2 ]) materials consisting of two or more...

...Hao Dong; Bin Zhao; Jianhua Xie The application of Hopf bifurcation is essential to rail vehicle dynamics because it corresponds to the linear critical speed. In engineering, researchers always wonder which vehicle parameters are sensitive to it. With the nonlinear singularity theory's development...

...Liangqiang Zhou; Fangqi Chen Subharmonic bifurcations and chaotic dynamics are investigated both analytically and numerically for a class of ship power system. Chaos arising from heteroclinic intersections is studied with the Melnikov method. The critical curves separating the chaotic...

... equations. A bifurcation analysis has been carried out considering the amplitude of the wing actuation force as the control parameter to investigate different complex states of the system. Interesting dynamical behavior including period doubling, chaotic transients, periodic windows, and finally...

... in the J OURNAL OF C OMPUTATIONAL AND N ONLINEAR D YNAMICS . Manuscript received June 4, 2017; final manuscript received September 7, 2017; published online November 1, 2017. Assoc. Editor: Corina Sandu. 04 06 2017 07 09 2017 Bifurcations Chaotic dynamics Fractional calculus...

... degenerate grazing bifurcations, we show how to obtain the degenerate grazing points of the 1/n impact periodic motions by the existence and stability analysis first. Then, a discrete-in-time feedback control strategy is used to suppress the grazing-induced chaos into the 1/n impact periodic motions...

..., observability constants, and bifurcation diagram have been exploited. The results of these calculations verify the specific features of the new system and further determine the effect of different system parameters on its dynamics. The proposed system has been experimentally implemented as an analog circuit...

...Antonio Simon Chong Escobar; Piotr Brzeski; Marian Wiercigroch; Przemyslaw Perlikowski In this paper, we perform a path-following bifurcation analysis of church bell to gain an insight into the governing dynamics of the yoke–bell–clapper system. We use an experimentally validated hybrid dynamical...