... proportional-derivative (PD) controller is introduced. Second, by analyzing the characteristic equation, the conditions for Hopf bifurcation and Turing instability of the controlled network model are obtained. Furthermore, the amplitude equation of the controlled neural network is obtained based...

.... Furthermore, we perform a nonlinear analysis of the system and observe the existence of sub and supercritical Hopf bifurcation with or without any nonlinearity in the friction isolator. However, the region of sub and supercritical Hopf bifurcation on stability curves depends on the nonlinearity in FI...

... of multiple delays on the local stability and Hopf bifurcation of the system are explored by selecting the sum of delays as bifurcation parameter and discussing the related characteristic equations. It is found that the dynamic behaviors of the system depend on the critical value of bifurcation. In addition...

....com 16 04 2019 20 11 2019 16 01 2020 fractional-order system delays food chain model Hopf bifurcation Since the seminal work on the susceptible-infective-removal epidemic model and predator–prey model, mathematical biology has been intensively investigated...

...-mail:  james.chagdes@miamioh.edu 03 10 2018 16 01 2019 09 09 2019 human upright posture stability balance board numerical nonlinear analysis Hopf bifurcation pitchfork bifurcation DDE-BifTool® Balance boards (BBs) are surfaces that rotate with their center of mass (CoM) located...

... D YNAMICS . Manuscript received April 24, 2018; final manuscript received March 26, 2019; published online May 13, 2019. Assoc. Editor: Eihab Abdel-Rahman. 24 04 2018 26 03 2019 chaotic jerk oscillator Hopf bifurcation self-excited and hidden attractors antimonotonicity...

... the suspension and steering system. Based on the dynamic model, the Hopf bifurcation theory is used to qualitatively analyze the existence of the limit cycle for the vehicle shimmy system, and the multiple limit cycle shimmy phenomenon is successfully reproduced using a numerical method. Moreover, the effect...

...-domain simulations are performed to investigate LCOs while continuation tools are employed to path follow the post-critical LCOs. A supercritical Hopf bifurcation behavior, confirmed by a stable LCO, is found past the critical flutter condition. The analysis shows that the LCO amplitude increases...

.... Assoc. Editor: Dr. Corina Sandu. 07 07 2013 12 05 2014 11 02 2015 Roller rig tests were adopted to illustrate two typical types of Hopf bifurcations existing in the railway vehicles. In order to investigate the influence of the vehicles' parameters on the features of Hopf...

... the values of the connecting spring constants may affect the excitation frequency range of ILMs and cause Hopf bifurcation to occur, followed by amplitude modulated motions (AMMs) including chaotic vibrations. The influence of the imperfections of the pendula on the system response is also investigated...

.... , and Balachandran , B. , 1995 , Applied Nonlinear Dynamics , John Wiley and Sons , New York . [9] Nayfeh , A. H. , and Balachandran , B. , 1990 , “ Motion Near a Hopf Bifurcation of a Three-Dimensional System ,” Mech. Res. Commun. , 17 ( 4 ), pp. 191 – 198 . 10.1016/0093-6413(90)90078-Q...

... ¯ i elongate, and ILMs occur at a wider excitation frequency range than in Fig. 12 . Hopf bifurcations occur at points G ¯ i and H ¯ i on branches b ¯ i , and AMMs appear over interval G ¯ i H ¯ i...

...) that amplitude modulated motions (AMMs) appear within these portions and the vertical thin line “|” denotes the magnitude of the modulated amplitudes. Therefore, it is concluded that points I i and J i are Hopf bifurcation points. The results of the numerical simulation are plotted only when (1,0) mode...

... vibrate at low amplitudes, even if the dimensions of the NTMDs are identical. Namely, “localization phenomenon” or “mode localization” occurs. After the pitchfork bifurcation, Hopf bifurcations may occur depending on the values of the system parameters, and amplitude- and phase-modulated motions...