Bifurcations and chaos in a discrete SI epidemic model with fractional order by Mahmoud A. M. Abdelaziz, Ahmad Izani Ismail, Farah A. Abdullah, Mohd Hafiz Mohd

“…By using the center manifold theorem and bifurcation theory, it is shown that the model undergoes flip and Neimark–Sacker bifurcation. …”
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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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Mixed Fourier-Legendre Spectral Methods for the Multiple Solutions of the Schrodinger Equation on the Unit Disk by Zhao-Xiang Li, Ji Lao, Zhong-Qing Wang

“…In this paper, we first compute the multiple non-trivial solutions of the Schrodinger equation on a unit disk, by using the Liapunov-Schmidt reduction and symmetry-breaking bifurcation theory, combined with the mixed Fourier-Legendre spectral and pseudospectral methods. …”
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Neimark–Sacker bifurcation of a chemotherapy treatment of glioblastoma multiform (GBM) by F. Bozkurt, A. Yousef

“…Moreover, we use the center manifold theorem and bifurcation theory to show that the model undergoes Neimark–Sacker bifurcation. …”
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Bifurcation analysis of a modified Leslie–Gower model with Holling type-IV functional response and nonlinear prey harvesting by Zizhen Zhang, Ranjit Kumar Upadhyay, Jyotiska Datta

“…We study the model system using qualitative analysis, bifurcation theory and singular optimal control. We show that the interior equilibrium point is locally asymptotically stable and the system under goes a Hopf bifurcation with respect to the ratio of intrinsic growth of the predator and prey population as bifurcation parameter. …”
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Degenerated Bogdanov-Takens bifurcations in an immuno-tumor model by Mariana P. Trifan, Adelina Georgescu

“…Kuznetsov [<i>Elements of applied bifurcation theory</i> (1994)], based on an appropriate splitting of associated Hilbert spaces. …”
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Bifurcations and chaos in a three-dimensional generalized Hénon map by Jingjing Zheng, Ziwei Wang, You Li, Jinliang Wang

“…According to the center manifold theorem and bifurcation theory, we get the existence conditions for fold bifurcation, flip bifurcation, and Naimark–Sacker bifurcation of the system. …”
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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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Business success of an environmental organization by Trukhanov Dmitry, Pryakhin Gennadiy

“…For example, the study of organizations using bifurcation theory is almost entirely absent in modern literature and scientific publications. …”
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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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Bifurcation analysis in a discrete predator–prey model with herd behaviour and group defense by Jie Xia, Xianyi Li

“…Specifically, some new results for the transcritical bifurcation, the period-doubling bifurcation, and the Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. Novelty includes a smooth transition from individual behaviour (low number of prey) to herd behaviour (large number of prey). …”
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Analysis of loan benchmark interest rate in banking loan dynamics: bifurcation and sensitivity analysis by Moch. Fandi Ansori, Nurcahya Yulian Ashar

“…We study the loan equilibrium's stability via bifurcation theory. It is found that the benchmark rate must be set between the flip and transcritical values. …”
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Small amplitude periodic solution of Hopf Bifurcation Theorem for fractional differential equations of balance point in group competitive martial arts by Chen Shuang, Ren Yuanjin

“…Through delay differential equation theory and Hopf bifurcation theory, the stability of the equilibrium point and the existence of periodic solutions generated by the Hopf bifurcation caused by the ‘instability’ of the equilibrium point are discussed. …”
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Bifurcations and chaos in a novel discrete economic system by A Al-khedhairi, AE Matouk, SS Askar

“…Existence of chaotic dynamics in the proposed game is also shown via two routes: Neimark–Sacker bifurcation and flip bifurcation. Based on the bifurcation theory of discrete-time systems, sufficient conditions of transcritical bifurcation are derived and applied to the proposed model. …”
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Dynamics and Bifurcations of a Discrete-Time Moran-Ricker Model with a Time Delay by Bo Li, Zimeng Yuan, Zohreh Eskandari

“…Bifurcations associated with flipping, doubling, and Neimark–Sacker for codimension-one (codim-1) model can be analyzed using bifurcation theory and the normal form method. We also investigate codimension-two (codim-2) bifurcations corresponding to 1:2, 1:3, and 1:4 resonances. …”
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Collective Power: Minimal Model for Thermodynamics of Nonequilibrium Phase Transitions by Tim Herpich, Juzar Thingna, Massimiliano Esposito

“…Our work shows the way towards building a thermodynamics of nonequilibrium phase transitions in conjunction with the bifurcation theory.…”
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Bifurcation and Chaos of a Nonlinear Discrete-Time Predator-Prey Model Involving the Nonlinear Allee Effect by Ning Song

“…Second, we establish a model with the Allee effect in prey undergoing codimension-one bifurcations (flip bifurcation and Neimark–Sacker bifurcation) and codimension-two bifurcation associated with 1 : 2 strong resonance by using center manifold theorem and bifurcation theory, and the direction of bifurcations is also evaluated. …”
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Investigation of Gyroscopic Effect on the Stability of High Speed Micromilling via Bifurcation Analysis by Rinku K. Mittal, Ramesh K. Singh

“…This study uses the multiple degrees of freedom (MDOF) model of the cutting tool to investigate the gyroscopic effect in machining. Hopf bifurcation theory is used to understand the long-term dynamic behavior of the system. …”
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