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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mussel-algae model, brownian motion, regime switching, extinction, ergodic stationary distribution by Menghan Chen, Haihong Liu, Ruiqi Wang

“…First, for the protein production time delay, a critical value is given by Hopf bifurcation theory. It is found that a larger time delay can lead to a larger amplitude and a longer period. …”
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Mathematical Model for the Biological Control of the Coffee Berry Borer <i>Hypothenemus hampei</i> through Ant Predation by Carlos Andrés Trujillo-Salazar, Gerard Olivar-Tost, Deissy Milena Sotelo-Castelblanco

“…Mathematically, the system’s equilibrium points were determined, and its stability was studied through qualitative theory. Bifurcation theory and numerical simulations were applied to illustrate the stability of the results, which were interpreted as conditions of the coexistence of the species, as well as conditions for eradicating the pest, at least theoretically, through biocontrol action in combination with other actions focused on eliminating only adult CBBs.…”
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Early warning signals have limited applicability to empirical lake data by Duncan A. O’Brien, Smita Deb, Gideon Gal, Stephen J. Thackeray, Partha S. Dutta, Shin-ichiro S. Matsuzaki, Linda May, Christopher F. Clements

“…Our results suggest that predictive ecology should start to move away from the concept of critical transitions, developing methods suitable for predicting resilience loss not limited to the strict bounds of bifurcation theory.…”
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Bifurcation analysis, chaotic structures and wave propagation for nonlinear system arising in oceanography by Karmina K. Ali, Waqas Ali Faridi, Abdullahi Yusuf, Magda Abd El-Rahman, Mohamed R. Ali

“…The equation is transformed into a planar dynamical structure through the Galilean transformation. By utilizing bifurcation theory, the potential phase portraits of nonlinear and super-nonlinear traveling wave solutions are investigated. …”
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Dynamic behavior of P53-Mdm2-Wip1 gene regulatory network under the influence of time delay and noise by LanJiang Luo, Haihong Liu, Fang Yan

“…Then we study the stability of the system and the existing conditions of Hopf bifurcation by using Hopf bifurcation theory with time delays as the bifurcation parameter. …”
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Complex Dynamic Behaviors of a Modified Discrete Leslie–Gower Predator–Prey System with Fear Effect on Prey Species by Sijia Lin, Fengde Chen, Zhong Li, Lijuan Chen

“…Subsequently, we discuss flip bifurcation, transcritical bifurcation at the equilibria of the system, by using the center manifold theorem and bifurcation theory. We find that system changes from chaotic state to four-period orbit, two-period orbit, stable state, and finally prey species will be driven to extinction, while predator species survive in a stable state for enough large birth rate of prey species with the increasing of fear effect. …”
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Operational Stability of Hydropower Plant with Upstream and Downstream Surge Chambers during Small Load Disturbance by Yi Liu, Xiaodong Yu, Xinlei Guo, Wenlong Zhao, Sheng Chen

“…Subsequently, the operational stability and nonlinear dynamic behavior of the HPUDSC system were studied based on Hopf bifurcation theory and numerical simulation. Finally, the influencing factors of stability of the HPUDSC system were investigated. …”
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Experimental and Numerical Analysis of Torsional—Lateral Vibrations in Drive Lines Supported by Hydrodynamic Journal Bearings by Fabrizio Antonio Stefani, Carlo Alberto Niccolini Marmont Du Haut Champ, Paolo Silvestri, Aristide Fausto Massardo

“…A hypothesis based on Hopf bifurcation theory (HBT), which justifies how the coupling phenomenon develops, is validated by means of overall experimental observations and a suitable numerical model. …”
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Phase portraits and optical soliton solutions of coupled Sasa–Satsuma model in birefringent fibers by Zhao Li, Wenjie Fan, Fang Miao, Changjiang Jin

“…According to the bifurcation theory of planar dynamical system, the phase portrait of two-dimensional dynamical system is drawn. …”
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Nonlinear Dynamics of Pilot-Operated Hydraulic Control Valves for Submersible Based on Improved Newmark- Integration Method<italic/> by Shuxun Li, Yu Zhang, Chao Lian, Jianjun Hou

“…A direction is provided for the applied research of nonlinear system bifurcation theory in self-operated valves.…”
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Mathematical analysis of robustness of oscillations in models of the mammalian circadian clock. by Xiangyu Yao, Benjamin L Heidebrecht, Jing Chen, John J Tyson

“…In this paper, we use bifurcation theory to explore mathematical models of genetic oscillators, based on Kim & Forger's interpretation of the circadian clock in mammals. …”
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Simulation of the poly- and monodispersed granular material. Part II: the stability state characterization / Daugiadispersio ir viendispersio dalelių mišinio elgsenos tyrimas. II d... by Gvidas Pocius, Robertas Balevičius

“…For the interpretation of these textures, Shilnikov's homoclinic bifurcation theory was discussed and applied. In particular, it was found that textures specifying the quasistatic state mainly resulted from the resonant effect depending on the degree of freedom of the analyzed particles. …”
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Bifurcation Behavior and Hybrid Controller Design of a 2D Lotka–Volterra Commensal Symbiosis System Accompanying Delay by Qingyi Cui, Changjin Xu, Wei Ou, Yicheng Pang, Zixin Liu, Peiluan Li, Lingyun Yao

“…Making use of stability and bifurcation theory of delayed differential equation, we focus on the emergence of bifurcation behavior and stability nature of the formulated delayed Lotka–Volterra commensal symbiosis system. …”
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Eddy viscosity modeling around curved boundaries through bifurcation approach and theory of rotating turbulence by Toh, Yi Han, Ng, Bing Feng

“…A novel approach to curvature effects based on the bifurcation theory and rotation turbulence energy spectrum is implemented to improve the sensitivity of the k−ϵ two-equation turbulence model (Jones-Launder form) to curved surfaces. …”
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Schistosomiasis model with treatment, habitat modification and biological control by Wahyudin Nur, Trisilowati, Agus Suryanto, Wuryansari Muharini Kusumawinahyu

“…Linearization combined with the Routh-Hurwitz criterion is used to prove the local stability condition of disease-free equilibrium points. Bifurcation theory is applied to investigate the local stability condition of the endemic equilibrium points. …”
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