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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SEBUAH MODEL CUSP CATASTROPHE UNTUK KECERDASAN by Asti Meiza Abdullah

“…Especially in mathematical understanding, catastrophe theory is a part of singularities theory and bifurcation theory.</em></p><p><em>The samples were the psychological testing, IST, results of 428 ITB's students. …”
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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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The effect of parameters on positive solutions and asymptotic behavior of an unstirred chemostat model with B–D functional response by Xiaozhou Feng, Suping Sun, Tongqian Zhang, Xiaomin An

“…The main methods used in this paper include the fixed point index theory, bifurcation theory, perturbation technique, comparison principle, and persistence theorem.…”
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Aircraft wing rock dynamics and control by Go, Tiauw Hiong

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Global and local excitation and inhibition shape the dynamics of the cortico-striatal-thalamo-cortical pathway by Anca Rădulescu, Joanna Herron, Caitlin Kennedy, Annalisa Scimemi

“…Here we use non-linear modeling of neuronal activity and bifurcation theory to investigate how global and local changes in E/I of MSNs regulate the activity of the CSTC pathway. …”
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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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The Qualitative Analysis of a Lorenz-Type System by A. A. Abramchenko, A. N. Kanatnikov

“…Effective qualitative analysis of differential equations systems is best approached through the bifurcation theory which explains modification of quality in the behaviour of a dynamic system if its parameters are changed.In the behavior of dynamic systems, in addition to the equilibrium points, other bounded trajectories (for example, boundary cycles or separatrix) and their certain conglomerates (such as attractors, invariant tori) play an important role. …”
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Slow and soft passage through tipping point of the Atlantic Meridional Overturning Circulation in a changing climate by Soong-Ki Kim, Hyo-Jeong Kim, Henk A. Dijkstra, Soon-Il An

“…Abstract Paleo-proxy records suggest that the Atlantic Meridional Overturning Circulation (AMOC) exhibits a threshold for an abrupt change, a so-called tipping point. A classical bifurcation theory, a basis of the tipping dynamics of AMOC implicitly assumes that the tipping point is fixed. …”
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Dynamics analysis of the hybrid powertrain under multi-frequency excitations with two time scales by Donghai Hu, Yanzhi Yan, Xiaoming Xu, Jing Wang

“…The dynamic equations under different excitation frequencies and amplitudes are obtained. Bifurcation theory is applied to study the bifurcation behavior when the equilibrium point is unstable, and the conditions for the generation of fold bifurcation are derived. …”
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Subharmonic solutions for a class of predator-prey models with degenerate weights in periodic environments by López-Gómez Julián, Muñoz-Hernández Eduardo, Zanolin Fabio

“…By means of a topological approach based on techniques from global bifurcation theory, the first part of the paper ascertains their nature, multiplicity and minimal complexity, as well as their global minimal structure, in terms of the configuration of the function coefficients in the setting of the model. …”
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The Qualitative Analysis of a Lorenz-Type System by A. A. Abramchenko, A. N. Kanatnikov

“…Effective qualitative analysis of differential equations systems is best approached through the bifurcation theory which explains modification of quality in the behaviour of a dynamic system if its parameters are changed.…”
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Mathematical Modeling and Stability Analysis of a Delayed Carbon Absorption-Emission Model Associated with China’s Adjustment of Industrial Structure by Leilei Han, Haokun Sui, Yuting Ding

“…We also analyze the characteristic roots of the characteristic equation at each equilibrium point for the model, then, we analyze the stability of the equilibrium point for the model according to the characteristic root, and discuss the existence of Hopf bifurcation of the system by using bifurcation theory. Secondly, we derive the normal form of Hopf bifurcation by using the multiple time scales method. …”
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Stability and bifurcation analysis of a discrete Leslie predator-prey system via piecewise constant argument method by Saud Fahad Aldosary, Rizwan Ahmed

“…It was shown that the system experienced period-doubling (PD) and Neimark-Sacker (NS) bifurcations at the positive fixed point by using the center manifold and bifurcation theory. The management of the system's bifurcating and fluctuating behavior may be controlled via the use of feedback and hybrid control approaches. …”
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Global dynamics, Neimark-Sacker bifurcation and hybrid control in a Leslie’s prey-predator model by A.Q. Khan, S.A.H. Bukhari, M.B. Almatrafi

“…Further for the discrete-time Leslie’s prey-predator model, existence of periodic points are also investigated. By bifurcation theory, it is also proved that if (a,b,c,d,h,α)∈NSBExy+aαcd+bα,adcd+bα then at interior fixed point: Exy+aαcd+bα,adcd+bα, discrete Leslie’s prey-predator model undergo Neimark-Sacker bifurcation and no other bifurcation occurs at it. …”
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