A simplified model of the Martian atmosphere - Part 2: a POD-Galerkin analysis by S. G. Whitehouse, S. R. Lewis, I. M. Moroz, P. L. Read

“…We investigate each in turn, using tools from bifurcation theory, to determine which of the systems most closely resembles the data for which the original diagnostics were performed.…”
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A simplified model of the Martian atmosphere - Part 2: a POD-Galerkin analysis by Whitehouse, S, Lewis, S, Moroz, I, Read, P

“…We investigate each in turn, using tools from bifurcation theory, to determine which of the systems most closely resembles the data for which the original diagnostics were performed.…”

Dynamic behaviors of a discrete-time predator–prey bioeconomic system by Weiyi Liu, Donghan Cai, Jie Shi

“…Also the dynamic behaviors of the system are investigated, by using normal form theory, center manifold theorem and bifurcation theory, it is shown that the system undergoes a Neimark–Sacker bifurcation and a flip bifurcation, on varying step-size in some range. …”
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Investigation on dynamics of an impulsive predator–prey system with generalized Holling type IV functional response and anti-predator behavior by Sekson Sirisubtawee, Nattawut Khansai, Akapak Charoenloedmongkhon

“…Violating such a condition, the system turns out to be permanent. Employing bifurcation theory, some conditions, under which the existence and stability of a positive periodic solution of the system occur but its prey-eradication periodic solution becomes unstable, are provided. …”
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Simulation Study of the Variations in Driving Pressure and Frequency on Microbubbles Contras Agents Behavior by Aladdin M. Hasson, Abdulkarim H. Dagher, Bassam T. Mohammad

“…In this simulation study the effects of pressure and frequency as influential factors on the stability of the microbubble were studied in wide range (frequencies are extend from f<fr to f≈3 fr, pressure extends from 0.05 to 1.5 MPa.), and analyzed using the bifurcation theory to visualize and characterize the effect of these factors on the microbubbles behavior. …”
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Bifurcation and chaos in a discrete predator-prey system of Leslie type with Michaelis-Menten prey harvesting by Chen Jialin, Zhu Zhenliang, He Xiaqing, Chen Fengde

“…It is shown that the system can undergo fold bifurcation, flip bifurcation, and Neimark-Sacker bifurcation by using the center manifold theorem and bifurcation theory. Numerical simulations are presented to illustrate the main theoretical results. …”
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Rabinowitz Alternative for Non-cooperative Elliptic Systems on Geodesic Balls by Rybicki Sławomir, Shioji Naoki, Stefaniak Piotr

“…Since the problem is variational and SO⁡(n){\operatorname{SO}(n)}-symmetric, we apply the techniques of equivariant bifurcation theory to prove the main results of this article. …”
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Bifurcation Analysis of a Certain Hodgkin-Huxley Model Depending on Multiple Bifurcation Parameters by André H. Erhardt

“…To this aim, we study the dynamics of the model using bifurcation theory and numerical bifurcation analysis. Furthermore, we investigate the interaction of the potassium and calcium current. …”
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Bifurcation analysis and chaos control in discrete-time modified Leslie–Gower prey harvesting model by Muhammad Bilal Ajaz, Umer Saeed, Qamar Din, Irfan Ali, Muhammad Israr Siddiqui

“…Furthermore, with the help of bifurcation theory and center manifold theorem, existence and directions of period-doubling and Neimark–Sacker bifurcations are investigated at positive steady-state. …”
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Dynamics of a three-molecule autocatalytic Schnakenberg model with cross-diffusion: Turing patterns of spatially homogeneous Hopf bifurcating periodic solutions by Weiyu Li, Hongyan Wang

“…First, utilizing the local Hopf bifurcation theory, the central manifold theory, the normal form method and the regular perturbation theory of the infinite dimensional dynamical system, the stability of periodic solutions for the ODE system is discussed. …”
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Data-driven discovery and extrapolation of parameterized pattern-forming dynamics by Zachary G. Nicolaou, Guanyu Huo, Yihui Chen, Steven L. Brunton, J. Nathan Kutz

“…First-principles derivations of the underlying transitions can be characterized using bifurcation theory on model systems whose governing equations are known. …”
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Behavior Analysis of a Class of Discrete-Time Dynamical System with Capture Rate by Xiongxiong Du, Xiaoling Han, Ceyu Lei

“…By using the center manifold theorem and bifurcation theory, the conditions for the existence of flip bifurcation and Hopf bifurcation in the interior of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>R</mi><mrow><mo>+</mo></mrow><mn>2</mn></msubsup></semantics></math></inline-formula> are proved. …”
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Modeling and Dynamical Analysis of a Fractional-Order Predator–Prey System with Anti-Predator Behavior and a Holling Type IV Functional Response by Baiming Wang, Xianyi Li

“…Then, we analyze the stability of its equilibrium points and the possibility of bifurcations using stability analysis methods and bifurcation theory, demonstrating that, under specific parameter conditions, the continuous system exhibits a Hopf bifurcation, while the discrete version exhibits a Neimark–Sacker bifurcation and a period-doubling bifurcation. …”
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Mechanistically derived Toxicant-mediated predator-prey model under Stoichiometric constraints by Md Nazmul Hassan, Angela Peace

“…Analytic, numerical, slow-fast steady state and bifurcation theory are employed to predict the risk of toxicant bio-accumulation under varying food conditions. …”
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A review on modelling techniques for formability prediction of sheet metal forming by Ruiqiang Zhang, Zhutao Shao, Jianguo Lin

“…These modelling techniques are primarily developed based on bifurcation theory, geometrical imperfection theory and continuum damage mechanics. …”
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Modeling the Dynamics of Arboviral Diseases with Vaccination Perspective by Hamadjam Abboubakar, Jean Claude Kamgang, Nkague Leontine Nkamba, Daniel Tieudjo, Lucas Emini

“…A qualitative analysis based on stability and bifurcation theory reveals that the phenomenon of backward bifurcation may occur; the stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the associated reproduction number is less than unity. …”
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Multiple bifurcations of a discrete modified Leslie-Gower predator-prey model by Yajie Sun, Ming Zhao, Yunfei Du

“…The existence and local stability of the fixed points of this system are studied. According to bifurcation theory and normal forms, we investigate the codimension 1 and 2 bifurcations of positive fixed points, including the fold, 1:1 strong resonance, fold-flip and 1:2 strong resonance bifurcations. …”
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Neimark–Sacker Bifurcation of a Discrete-Time Predator–Prey Model with Prey Refuge Effect by Binhao Hong, Chunrui Zhang

“…The existence and stability of the three equilibria are analyzed, and the formation conditions of Neimark–Sacker bifurcation around the unique positive equilibrium point are established using the center manifold theorem and bifurcation theory. An attracting closed invariant curve appears, which corresponds to the periodic oscillations between predators and prey over a long period of time. …”
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Stability, bifurcation, and chaos control in a discrete predator-prey model with strong Allee effect by Ali Al Khabyah, Rizwan Ahmed, Muhammad Saeed Akram, Shehraz Akhtar

“…Furthermore, the existence and direction of period-doubling and Neimark-Sacker bifurcations are explored at the interior fixed point using bifurcation theory and the center manifold theorem. A hybrid control method is used for controlling chaos and bifurcations. …”
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Dynamical Behaviors in a Stage-Structured Model with a Birth Pulse by Yun Liu, Lifeng Guo, Xijuan Liu

“…Through the application of the center manifold theorem and bifurcation theory, our research has shown that the given model exhibits transcritical and flip bifurcation near its interior equilibrium point. …”
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