Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges by Wei Li, Chunrui Zhang, Mi Wang

“…The critical coefficients and properties of bifurcating periodic solutions for Flip and Hopf bifurcations are computed using the center manifold theorem and bifurcation theory. Additionally, numerical simulations are employed to illustrate the bifurcation phenomenon and chaos characteristics. …”
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Stability and Bifurcation for a Delayed Diffusive Two-Zooplankton One-Phytoplankton Model with Two Different Functions by Xin-You Meng, Li Xiao

“…Furthermore, due to the local bifurcation theory of partial functional differential equations, Hopf bifurcation of the model is investigated by considering time delay as the bifurcation parameter. …”
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Stability and Hopf Bifurcation in a Three-Component Planktonic Model with Spatial Diffusion and Time Delay by Kejun Zhuang, Gao Jia, Dezhi Liu

“…Then, the stability of constant equilibrium solution and occurrence of Hopf bifurcation are detailed and analyzed by using the bifurcation theory. Moreover, the formulas for determining the bifurcation direction and stability of spatially bifurcating solutions are derived. …”
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Bifurcations and Dynamics of the Rb-E2F Pathway Involving miR449 by Lingling Li, Jianwei Shen

“…We focused on the gene regulative network involving Rb-E2F pathway and microRNAs (miR449) and studied the influence of time delay on the dynamical behaviors of Rb-E2F pathway by using Hopf bifurcation theory. It is shown that under certain assumptions the steady state of the delay model is asymptotically stable for all delay values; there is a critical value under another set of conditions; the steady state is stable when the time delay is less than the critical value, while the steady state is changed to be unstable when the time delay is greater than the critical value. …”
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Multiple Nonlinear Oscillations in a 𝔻3×𝔻3-Symmetrical Coupled System of Identical Cells with Delays by Haijun Hu, Li Liu, Jie Mao

“…We also investigate the simultaneous occurrence of multiple periodic solutions and spatiotemporal patterns of the bifurcating periodic oscillations by using the equivariant bifurcation theory of delay differential equations combined with representation theory of Lie groups. …”
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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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Chaos and bifurcation analysis of tumor-immune controlled system with time delay by Danni Wang, Hongli Yang, Liangui Yang

“…The Flip bifurcation and Neimark–Sacker bifurcation of system are proved by the normal form method, central manifold theorem, and bifurcation theory. The Gram–Schmidt orthonormalization (GSO) method is used to interpret the attractor properties of uncontrolled and controlled systems, it is revealed that the attractors of controlled systems are smaller than those of uncontrolled systems, and the theoretical and numerical results are consistent. …”
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Neimark–Sacker Bifurcation and Controlling Chaos in a Three-Species Food Chain Model through the OGY Method by Guo Feng, Ding Yin, Li Jiacheng

“…The dynamics behavior of a discrete-time three-species food chain model is investigated. By using bifurcation theory, it is shown that the equilibrium point of the system loses its stability, and the system undergoes Neimark–Sacker bifurcation, which leads to chaos as the parameter changes. …”
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Bifurcation Analysis and Chaos Control in a Discrete-Time Parasite-Host Model by Xueli Chen, Lishun Ren

“…The existence and stability of nonnegative fixed points are explored and the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. And we also prove the chaos in the sense of Marotto. …”
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Complex Dynamical Behaviors in a Predator-Prey System with Generalized Group Defense and Impulsive Control Strategy by Shunyi Li

“…Otherwise, the system is permanent if the impulsive period is larger than the critical value. By using bifurcation theory, we show the existence and stability of positive periodic solution when the pest eradication lost its stability. …”
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Extinction and Permanence of a General Predator-Prey System with Impulsive Perturbations by Xianning Liu, Lansun Chen

“…The existence of a positive periodic solution is also studied by the bifurcation theory. Application is given to a Lotka-Volterra predator-prey system with periodic impulsive immigration of the predator. …”
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Integrability, Variational Principle, Bifurcation, and New Wave Solutions for the Ivancevic Option Pricing Model by A. A. Elmandouh, M. E. Elbrolosy

“…He’s variational method is utilized to create new abundant solutions, which contain the bright soliton, bright-like soliton, kinky-bright soliton, and periodic solution. The bifurcation theory is applied to investigate the phase portrait and to study some dynamical behavior of this model. …”
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Z2×Z3 Equivariant Bifurcation in Coupled Two Neural Network Rings by Baodong Zheng, Haidong Yin

“…We discuss the spatiotemporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay differential equations combined with representation theory of Lie groups. …”
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Navier-Stokes: Singularities and Bifurcations by Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales

“…Through new theorems, we extend the theory of singularities in fluid dynamics and introduce quaternionic bifurcations, representing an innovative extension of classical bifurcation theory. Moreover, we delve into the investigation of the regularity of compressible fluids, exploring the conditions under which solutions remain smooth or develop singularities. …”
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Bifurcation Analysis of a Discrete Basener–Ross Population Model: Exploring Multiple Scenarios by A. A. Elsadany, A. M. Yousef, S. A. Ghazwani, A. S. Zaki

“…These criteria are derived using the center manifold theorem and bifurcation theory. Furthermore, we demonstrated the existence of codimension-two bifurcations characterized by 1:2, 1:3, and 1:4 resonances, emphasizing the model’s complex dynamical structure. …”
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Bifurcation and controller design in a 3D delayed predator-prey model by Jinting Lin, Changjin Xu, Yiya Xu, Yingyan Zhao, Yicheng Pang, Zixin Liu, Jianwei Shen

“…This paper determines the parameter conditions for system stability and the occurrence of bifurcations by employing bifurcation theory and the stability theory of delayed differential equations. …”
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Kinematic Singularity and Bifurcation Analysis of Sidestay Landing Gear Locking Mechanisms by Kui Xu, Yin Yin, Yixin Yang, Hong Nie, Xiaohui Wei

“…The present study is aimed at investigating the synchronous locking performance of the dual-sidestay landing gear based on the singularity and bifurcation theory. From the perspective of the kinematic mechanism, the reason for high sensitivity to structural dimensions in the locking process is explained, and the locked position is investigated by employing the numerical continuation method in the case of a single-sidestay landing gear. …”
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