一个阿贝尔积分根的数目的下界(A lower bound for the number of zeroes about an Abelian integral) by YANDong-mei(严冬梅), LÜDa-mei(吕大梅)

“…Hopf bifurcation is an important part of bifurcation theory of dynamical systems. Almost all known works are concerned with the bifurcation and number of limit cycles near a nondegenerate focus or center. …”
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Bifurcation of a discrete predator-prey model with increasing functional response and constant-yield prey harvesting by Jiange Dong, Xianyi Li

“…Mainly, by utilizing the center manifold theorem and the bifurcation theory some sufficient conditions are obtained for the saddle-node bifurcation and the flip bifurcation of this system to occur. …”
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Flip bifurcation and Neimark-Sacker bifurcation in a discrete predator-prey model with Michaelis-Menten functional response by Xianyi Li, Xingming Shao

“…Then, by using the center manifold theorem and bifurcation theory, we demonstrate that the system experiences a flip bifurcation and a Neimark-Sacker bifurcation at a fixed point when one of the parameters goes through its critical value. …”
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A six-direction absolute displacement sensor for time-delayed control based on quasi-zero-stiffness property by Guyue Jiao, Xiuting Sun

“…And then, by utilizing bifurcation theory and perturbation method, the structural parameters are optimized for the improvement of measurement accuracy. …”
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Qualitative Analysis of the Discretization of a Continuous Fractional Order Prey-Predator Model with the Effects of Harvesting and Immigration in the Population by Md. Jasim Uddin, Sarker Md. Sohel Rana

“…Using the central manifold and bifurcation theory, we provide evidence for NS and PD bifurcations. …”
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Codimension-two bifurcation analysis at an endemic equilibrium state of a discrete epidemic model by Abdul Qadeer Khan, Tania Akhtar, Adil Jhangeer, Muhammad Bilal Riaz

“…More precisely, we examined the codimension-two bifurcation analysis at an endemic equilibrium state associated with $ 1:2 $, $ 1:3 $ and $ 1:4 $ strong resonances by bifurcation theory and series of affine transformations. …”
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Global structure of positive solutions for third-order semipositone integral boundary value problems by Zhonghua Bi, Sanyang Liu

“…Our analysis mainly relied on the bifurcation theory.</p>…”
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Complicate dynamical analysis of a discrete predator-prey model with a prey refuge by A. Q. Khan, Ibraheem M. Alsulami

“…Further, by the bifurcation theory, we have studied flip bifurcation at boundary fixed point, and flip and hopf bifurcations at interior fixed point of the discrete model. …”
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Universal Bifurcation Chaos Theory and Its New Applications by Nikolai A. Magnitskii

“…It is shown analytically and numerically that in all considered systems of equations, further complication of the dynamics of solutions and the transition to chemical and biological turbulence is carried out in full accordance with the universal Feigenbaum-Sharkovsky-Magnitskii bifurcation theory through subharmonic and homoclinic cascades of bifurcations of stable limit cycles. …”
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Bifurcation analysis and exact solutions for a class of generalized time-space fractional nonlinear Schrödinger equations by Baojian Hong

“…Furthermore, by applying the bifurcation theory method, the periodic wave solutions and traveling wave solutions with the corresponding phase orbits are easily obtained. …”
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Dynamics of a Discrete Leslie–Gower Model with Harvesting and Holling-II Functional Response by Chen Zhang, Xianyi Li

“…In this paper, we dedicate ourselves to investigating the bifurcation problems of the discrete version of the model by using the Center Manifold Theorem and bifurcation theory, and obtain sufficient conditions for the occurrences of the transcritical bifurcation and Neimark–Sacker bifurcation, and the stability of the closed orbits bifurcated. …”
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Dynamics of a Beddington-DeAngelis type predator-prey system with constant rate harvesting by Jaeun Lee, Hunki Baek

“…Various dynamical behaviors of the system including saddle-node points and a cusp of codimension 2 are investigated by using the analysis of qualitative method and bifurcation theory. Also, it is shown that the system undergoes several kinds of bifurcation such as the saddle-node bifurcation, the subcritical and supercritical Hopf bifurcation, Bogdanov-Takens bifurcation by choosing the death rate of the predator and the harvesting rate of the prey as the bifurcation parameters. …”
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Period-doubling bifurcation and Neimark-Sacker bifurcation of a discrete predator-prey model with Allee effect and cannibalism by Zhuo Ba, Xianyi Li

“…Not only the existence and local stability of fixed points of the discret system are investigated, but more important, the sufficient conditions for the occurrence of its period-doubling bifurcation and Neimark-Sacker bifurcation are obtained using the center manifold theorem and local bifurcation theory. Finally some numerical simulations are given to illustrate the existence of Neimark-Sacker bifurcation. …”
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Further Results on Bifurcation for a Fractional-Order Predator-Prey System concerning Mixed Time Delays by Zhenjiang Yao, Bingnan Tang

“…Taking advantage of the stability criterion and bifurcation theory of fractional-order dynamical system and regarding time delay as bifurcation parameter, we establish a new delay-independent stability and bifurcation criterion for the involved fractional-order predator-prey system. …”
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Complicate dynamics of a discrete predator-prey model with double Allee effect by Shaosan Xia, Xianyi Li

“…Then, by using the center manifold theorem and bifurcation theory, the sufficient conditions for the occurrences of transcritical bifurcation and Neimark-Sacker bifurcation and the stability of closed orbit bifurcated are obtained. …”
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Transcritical bifurcation and Neimark-Sacker bifurcation of a discrete predator-prey model with herd behaviour and square root functional response by Danyang Li, Xianyi Li

“…Secondly, by employing the centre manifold theorem and bifurcation theory, the conditions for the occurrences of the transcritical bifurcation and Neimark-Sacker bifurcation are obtained. …”
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Hopf Bifurcation and Control for the Bioeconomic Predator–Prey Model with Square Root Functional Response and Nonlinear Prey Harvesting by Huangyu Guo, Jing Han, Guodong Zhang

“…The stability and Hopf bifurcation of the model are discussed through normal forms and bifurcation theory. These results reveal richer dynamic features of the bioeconomic predator–prey model which incorporates the square root functional response and nonlinear prey harvesting, and provides guidance for realistic harvesting. …”
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Loop Type Subcontinua of Positive Solutions for Indefinite Concave-Convex Problems by Kaufmann Uriel, Ramos Quoirin Humberto, Umezu Kenichiro

“…Our approach depends on local and global bifurcation analysis from the zero solution in a nonregular setting, since the nonlinearities considered are not differentiable at zero, so that the standard bifurcation theory does not apply. To overcome this difficulty, we combine a regularization scheme with a priori bounds, and Whyburn’s topological method. …”
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Bistability and Chaos Emergence in Spontaneous Dynamics of Astrocytic Calcium Concentration by Evgeniya V. Pankratova, Maria S. Sinitsina, Susanna Gordleeva, Victor B. Kazantsev

“…Using analytical and numerical analysis, various attracting sets were found and investigated. Employing bifurcation theory analysis, we examined steady state solutions, bistability, simple and complicated periodic limit cycles and also chaotic attractors. …”
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Bifurcations of a three-species prey-predator system with scavenger by Abdul Qadeer Khan, Syed Saqlain Kazmi, Turki D. Alharbi

“…In order to understand the dynamics of the understudied system thoroughly, we studied the occurrence of certain bifurcations at fixed points by the bifurcation theory. Finally, theoretical results are numerically verified.…”
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