... flip and Neimark–Sacker bifurcations. Moreover, codimension-two bifurcations of the endemic fixed point are discussed using bifurcation theory and normal forms. The model exhibits 1:2, 1:3, and 1:4 strong resonances. Numerical simulations are performed to verify our analysis. In addition, bifurcations...

... 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...

... delays, albeit very short in most cases, can give rise to irregular behaviors, such as different types of bifurcations of periodic orbits, quasi-periodic solutions, and even deterministic chaotic motions [ 10 , 16 – 18 ]. Neuronal networks with time delays, which are often described by delay differential...

...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...

... 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 are everywhere, especially in nature, e.g., see Refs. [ 1 – 5 ]. On the other hand...

.... 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...

.... Assoc. Editor: Dumitru Baleanu. 01 08 2017 21 03 2018 Bifurcations Chaotic dynamics Control Fractional calculus Nonlinear dynamical systems Nonlinear phenomena Stability of nonlinear systems The term “hidden attractor” was coined by Leonov et al. who discovered...

... of ASME for publication in the J OURNAL OF C OMPUTATIONAL AND N ONLINEAR D YNAMICS . Manuscript received December 23, 2017; final manuscript received June 7, 2018; published online July 2, 2018. Assoc. Editor: Eihab Abdel-Rahman. 23 12 2017 07 06 2018 Bifurcations Computational...

.... , and Ecker , H. , 1996 , “ Simulation of Nonlinear Dynamics in Magnetic Bearing ,” Computer Simulation Conference, Portland , OR, pp. 466–471. [2] Chinta , M. , and Palazzolo , A. B. , 1998 , “ Stability and Bifurcation of Rotor Motion in a Magnetic Bearing ,” J. Sound Vib. , 214 ( 5 ), pp...

... 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...

...) with matlab , the dynamic response of the suspension differential system can be obtained when the fractional order is q and under the condition of single frequency sinusoidal excitation. The x − q chaotic bifurcation diagram is obtained by continuously changing the fractional order q...

... 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...