Three people can synchronize as coupled oscillators during sports activities. by Keiko Yokoyama, Yuji Yamamoto

“…These results suggested that symmetric Hopf bifurcation theory could be used to understand synchronization phenomena among three people who communicate via perceptual information, not just physically connected systems such as slime molds, chemical reactions, and animal gaits. …”
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Stability and dynamic analysis of a grid-connected environmentally friendly photovoltaic energy system by Nasri, Shohreh, Zamanifar, Mehran, Naderipour, Amirreza, Nowdeh, Saber Arabi, Kamyab, Hesam, Abdul-Malek, Zulkurnain

“…To produce bifurcation diagrams based on the bifurcation theory, a parameter is constantly changed in each step, using MATLAB and AUTO, and eigenvalues are monitored simultaneously. …”

Thermodynamic and dynamical predictions for bifurcations and non-equilibrium phase transitions by Han Yan, Feng Zhang, Jin Wang

“…Such critical transitions in complex systems are commonly described as dynamical processes within the framework of nonlinear dynamics and the bifurcation theory. However, systematic treatment from the global thermodynamic perspective is still challenging. …”
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Delays and economic systems dynamics by Donatas Švitra

“…Analysis was made with the help of bifurcation theory.…”
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Modified logistic differential equation of neutral type with time delay by Donatas Švitra

“…The stable periodic solution based on the bifurcation theory of that differential equation is constructed. …”
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Mathematical analysis and simulation of Ebola virus disease spread incorporating mitigation measures by Roseline Toyin Abah, Abraham Baba Zhiri, Kayode Oshinubi, Adejimi Adeniji

“…The model’s equilibrium points are displayed and the effective basic reproduction number Reff is estimated. Bifurcation theory is used for the stability analysis of endemic equilibrium state and general bifurcation theory is used to prove the existence of endemic equilibrium state. …”
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Modified logistic differential equation of neutral type with time delay by Donatas Švitra

“…The stable periodic solution based on the bifurcation theory of that differential equation is constructed. …”
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Dynamics of a Prey-Predator System with Harvesting Effect on Prey by Özlem Ak Gümüş

“…Firstly, the existence and stability of the fixed points of the model are obtained, and then the presence and direction of Neimark-Sacker bifurcation is examined. By using the bifurcation theory, we show that the system undergoes Neimark-Sacker bifurcation. …”
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Stability and Hopf-bifurcation analysis of an unidirectionally coupled system by Gang Zhu, Junjie Wei

“…In this paper, the stability and existence of periodic solutions for an unidirectionally coupled nonlinear system with delays are investigated by combining the linear stability theory and the embedding technique of asymptotically autonomous semiflows, Hopf bifurcation theory and a continuation theorem of coincidence degree theory, respectively. …”
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Qualitative Analysis of a Nicholson-Bailey Model in Patchy Environment by Shehraz Akhtar, Rizwan Ahmed

“…Furthermore, Neimark-Sacker bifurcation is explored using the bifurcation theory of normal forms at interior steady-state. …”
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Dynamic analysis of an impulsively controlled predator-prey system by Hunki Baek

“…In addition, we show the existence and stability of a positive periodic solution by using bifurcation theory.…”
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Effects of cross-diffusion for a prey-predator system in a heterogeneous environment by Yaying Dong, Shanbing Li, Yanling Li

“…We first give the necessary condition and sufficient condition for the existence of coexistence states of the two species, by applying the bifurcation theory. Furthermore, the asymptotic behavior of coexistence states is established as the cross-diffusion coefficient of the prey tends to infinity. …”
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Multiple Hopf Bifurcations of Four Coupled van der Pol Oscillators with Delay by Liqin Liu, Chunrui Zhang

“…Secondly, the multiple periodic solutions of spatiotemporal patterns of the system are obtained by using symmetric Hopf bifurcation theory. The normal form of the system on the central manifold and the bifurcation direction of the bifurcating periodic solutions are derived. …”
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Neimark-Sacker bifurcation in a discrete dynamical model of population genetics by Attila Dénes

“…During computer experiments Tusnády discovered cyclic behaviour in the evolution of genotypes. Using bifurcation theory we prove that the system indeed can have cycles and this occurrence is caused by a Neimark-Sacker bifurcation.…”
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Dynamical Analysis of a Delayed Diffusive Predator–Prey Model with Additional Food Provided and Anti-Predator Behavior by Ruizhi Yang, Xiao Zhao, Yong An

“…The existence of Hopf bifurcation is also discussed based on the Hopf bifurcation theory. The property of Hopf bifurcation is derived through the theory of center manifold and normal form method. …”
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Stability and Neimark–Sacker Bifurcation of a Delay Difference Equation by Shaoxia Jin, Xianyi Li

“…Namely, some results for the existence and stability of Neimark–Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. Some numerical simulations are also given to validate the existence of the Neimark–Sacker bifurcation derived.…”
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Dynamic Analysis of the Project Investment Model with Time Delay and Density Constraints by Debao Gao

“…Second, the sufficiency of local asymptotic stability of the positive equilibrium point of the model is obtained by using the Hopf bifurcation theory and stability theory. Then, the formulas for determining the direction of Hopf bifurcation and the stability of the periodic solution are calculated by using the central manifold theory and normative theory. …”
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Control Analysis of Stochastic Lagging Discrete Ecosystems by Jinyi Zhang

“…Based on the stability and bifurcation theory of deterministic discrete systems, through mathematical analysis, asymptotic stability and Hopf bifurcation are existent in the ecosystem, constructing control functions, controlling the behavior of the system dynamics. …”
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FORECASTING FINANCIAL TIME SERIES USING A METHOD OF SELFORGANIZED CRITICALITY by Michail E. Mazurov

“…Giventhis mechanism to analyze the behaviorof financial time series, we use bifurcation theory and a system of nonlinear differential equations of parabolic type, which are thebasic equations in synergetics.…”
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Dynamics and optical soliton solutions in birefringent fibers for the coupled Kaup–Newell equation via planar dynamical system analysis method by Zhao Li

“…Secondly, the optical soliton solutions of the coupled Kaup–Newell equation are construct by the bifurcation theory of planar dynamical system together with the “three-step method” of Professor Li’s method. …”
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