Existence of Self-Excited and Hidden Attractors in the Modified Autonomous Van Der Pol-Duffing Systems by A. E. Matouk, T. N. Abdelhameed, D. K. Almutairi, M. A. Abdelkawy, M. A. E. Herzallah

“…In addition, conditions for approximating the solutions of the fractional version to periodic solutions are obtained via the Hopf bifurcation theory in fractional-order systems. Moreover, the technique for hidden attractors localization in the integer-order MAVPD is provided. …”
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Global bifurcation of positive solutions for a class of superlinear elliptic systems by Ruyun Ma, Yan Zhu, Yali Zhang

“…The proof of our main result is based upon bifurcation theory. In addition, as an application for our main result, when $f$ and $g$ subject to the upper growth bound, by a technique of taking superior limit for components, then we may show that the branch must bifurcate from infinity at $\lambda =0$.…”
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Multiple nontrivial solutions of superlinear fractional Laplace equations without (AR) condition by Zhao Leiga, Cai Hongrui, Chen Yutong

“…Our methods are the combination of minimax method, bifurcation theory, and Morse theory.…”
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Analysis of the Control Strategy of Non-linear Torsional Vibration in the Main Driving System of Cold Rolling Mill by He Yongling, Liao Binjie

“…Because Hopf bifurcation is one of the important reasons to the unstable oscillation of the main drive system of the rolling mill,it is necessary for effective control of the phenomenon of Hopf bifurcation. Based on Hopf bifurcation theory,a nonlinear state feedback controller is constructed. …”
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Hopf bifurcations in an atypical p53 protein oscillator model with discrete delay or distributed delay by Nan Liu, Hongli Yang, Liangui Yang

“…We focus on two types of time delays: discrete and distributed, use Hopf bifurcation theory to derive conditions for the occurrence of limit cycle oscillations, and confirm the properties of Hopf bifurcations by normal form and central manifold approaches. …”
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STUDY OF BIFURCATION ANALYSIS FOR DYNAMIC VOLTAGE STABILITY IN POWER SYSTEM by نیما امجدی, محمدرضا انصاری شهرضا

“…Student , Electrical & Computer Engineering Faculty, Semnan University, Semnan, Iran   * Corresponding Author: namjadi@semnan.ac.ir     Abstract   Voltage collapse is an inherently nonlinear phenomenon and it is suitable to use nonlinear analysis techniques such as bifurcation theory to study voltage collapse and to devise ways of avoiding it. …”
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Complex dynamics of a discrete predator–prey system with a strong Allee effect on the prey and a ratio-dependent functional response by Qiquan Fang, Xianyi Li

“…By using the center manifold theorem and bifurcation theory, we consider the flip bifurcation of this system at E1 $E_{1}$ and obtain the stability of the closed orbits bifurcated from E1 $E_{1}$. …”
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Novel corona virus disease dynamical models with pulse vaccination by Cheng’ao Li, Junliang Lu

“…Using the principle of stroboscopic mapping and the basic reproduction number R0, we show that if R0<1, the disease-free periodic solution is globally asymptotically stable; If R0>1, the model is persistent and there exists a positive periodic solution; Using the bifurcation theory, there is a supercritical bifurcation for the model if R0=1. …”
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Analysis and Control of Malware Mutation Model in Wireless Rechargeable Sensor Network with Charging Delay by Guiyun Liu, Zhimin Peng, Zhongwei Liang, Xiaojing Zhong, Xinhai Xia

“…With the condition of charging delay, the bifurcation phenomenon is investigated by using the Hopf bifurcation theory. Furthermore, to improve the security of WRSNs and decrease the control cost, the Pontryagin’s Maximum principle is applied to obtain an optimal control scheme under mutation and charging delay. …”
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Numerical bifurcation and hybrid control of a Gompertz model with time delay by Jizhi SONG, Yuanyuan WANG

“…The local stability of the equilibria is discussed according to Hopf bifurcation theory. For controlling Neimark-Sacker bifurcation, the hybrid control numerical algorithm is introduced to generate the Neimark-Sacker bifurcation at a desired bifurcation point. …”
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Research on Dynamic Parameters of a Passive Walking Robot with Flat Feet by Gao Jiachang, Gao Jianshe, Tao Zheng

“…The gait of the flat-foot robot's periodic motion is explained with the help of a stable limit cycle. Based on the bifurcation theory, the effects of the sole, heel, center of mass position, mass ration, and inclined plane inclination on the stable gait of the flat-foot robot are analyzed. …”
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Analytical bifurcation behaviors of a host–parasitoid model with Holling type III functional response by Ahmed M. Yousef, Saad Z. Rida, Soheir Arafat

“…More specifically, we used bifurcation theory and the center manifold theorem to prove that the model possess both period doubling and Neimark–Sacker bifurcations. …”
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On the non-autonomous Hopf bifurcation problem: systems with rapidly varying coefficients. by Matteo Franca, Russell Johnson

“…If the ODE is autonomous the supercritical Andronov–Hopf bifurcation theory gives sufficient conditions for the genesis of a repeller–attractor pair, made up by a critical point and a stable limit cycle respectively. …”
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Voltage Stability of Spacecraft Electric Power Systems for Deep Space Exploration by Marc A. Carbone, Amirhossein Sajadi, Jordan M. Murray, Jeffrey T. Csank, Kenneth A. Loparo

“…This paper provides an analysis of voltage stability of direct current (DC) microgrids for spacecraft applications. Bifurcation theory is used to determine the behavior of the system and identify the major causes of voltage instability. …”
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EVALUATION OF EFFECT OF REACTIVE POWER CONTROL STRATEGY BASED ON VOLTAGE TERMINAL OF GENERATORS ON LIMIT INDUCED BIFURCATION AND DYNAMIC VOLTAGE STABILITY MARGIN by M.H. Velayati, N. Amjady, I. Khajevandi

“…In this paper, based on a combined method include of time domain simulation, modal analysis and bifurcation theory effect of the regulation of terminal voltage of critical generators on the reactive power limit of generators and dynamic voltage stability status of power system based on the HB and LIB is evaluated. …”
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Codimension-Two Bifurcations of a Simplified Discrete-Time SIR Model with Nonlinear Incidence and Recovery Rates by Dongpo Hu, Xuexue Liu, Kun Li, Ming Liu, Xiao Yu

“…Here, using the integral step size and the intervention level as control parameters, we mainly discuss three types of codimension-two bifurcations (fold-flip bifurcation, 1:3 resonance, and 1:4 resonance) of the simplified discrete-time SIR model in detail by bifurcation theory and numerical continuation techniques. …”
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Dynamics Analysis of a Discrete-Time Commensalism Model with Additive Allee for the Host Species by Yanbo Chong, Ankur Jyoti Kashyap, Shangming Chen, Fengde Chen

“…Second, we used the center manifold theorem and bifurcation theory to study the bifurcation of a codimension of one of the system at non-hyperbolic fixed points, including flip, transcritical, pitchfork, and fold bifurcations. …”
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Dynamic complexity of a slow-fast predator-prey model with herd behavior by Ahmad Suleman, Rizwan Ahmed, Fehaid Salem Alshammari, Nehad Ali Shah

“…By employing the bifurcation theory, it is shown that the model undergoes both a period-doubling and a Neimark-Sacker bifurcation at the interior fixed point. …”
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Aircraft wing rock dynamics and control by Go, Tiauw Hiong

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Qualitative analysis and phase of chaos control of the predator-prey model with Holling type-III by Mohammed O. AL-Kaff, Hamdy A. El-Metwally, El-Metwally M. Elabbasy

“…The center manifold theorem and bifurcation theory are used to create existence conditions for flip bifurcations and Neimark-Sacker bifurcations. …”
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