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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Bifurcation analysis of a pair-wise epidemic model on adaptive networks by Jinna Lu, Xiaoguang Zhang

“…Moreover, we prove that the model exhibits transcritical forward bifurcation, backward bifurcation, saddle-node bifurcation and Hopf bifurcation using the methods of bifurcation theory. In addition, by a numerical example, the normal form of Hopf bifurcation and the first Lyapunov coefficient are derived, which show that a stable limit cycle can bifurcate from the endemic equilibrium with larger epidemicity. …”
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Dynamic behavior of the p53-Mdm2 core module under the action of drug Nutlin and dual delays by Juenu Yang, Fang Yan, Haihong Liu

“…The stability of the unique positive equilibrium point and the existence of Hopf bifurcation are studied by taking the time delays as the bifurcation parameters and applying bifurcation theory. Based on the normal form theory and central manifold theorem, explicit criteria to determine the Hopf bifurcation direction and stability of the bifurcated periodic solution are established. …”
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Global dynamics of an immunosuppressive infection model with stage structure by Hongying Shu, Zenghui Hao

“…Next, we conduct local and global Hopf bifurcation analysis for the proposed model via Hopf bifurcation theory of delay differential equations. We choose the delay as a bifurcation parameter and examine the onset and termination of Hopf bifurcations of periodic solutions from the immune control equilibrium. …”
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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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A Ratio-Dependent Nonlinear Predator-Prey Model With Certain Dynamical Results by Asifa Tassaddiq, Muhammad Sajjad Shabbir, Qamar Din, Khalil Ahmad, Sabeena Kazi

“…Moreover, existence of biologically feasible fixed points, their local asymptotic behavior and phase-plane classification of interior (positive) fixed point are carried out. Furthermore, bifurcation theory of normal forms is implemented to prove that proposed discrete-time model undergoes Neimark-Sacker bifurcation around its unique positive fixed point. …”
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A codimension-2 bifurcation controlling endogenous bursting activity and pulse-triggered responses of a neuron model. by William H Barnett, Gennady S Cymbalyuk

“…An open question is how temporal characteristics can be controlled in bursting activity and in transient neuronal responses to synaptic input. Bifurcation theory provides a framework to discover generic mechanisms addressing this question. …”
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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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Modeling Magnetomyograms of Uterine Contractions during Pregnancy Using a Multiscale Forward Electromagnetic Approach. by Mengxue Zhang, Vanessa Tidwell, Patricio S La Rosa, James D Wilson, Hari Eswaran, Arye Nehorai

“…At the cellular level, building on bifurcation theory, we apply generalized FitzHugh-Nagumo (FHN) equations that produces both plateau-type and bursting-type action potentials. …”
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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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Determinants of early afterdepolarization properties in ventricular myocyte models. by Xiaodong Huang, Zhen Song, Zhilin Qu

“…We first made predictions based on the bifurcation theory and then validated them in physiologically more detailed action potential models. …”
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Phase-locking patterns underlying effective communication in exact firing rate models of neural networks. by David Reyner-Parra, Gemma Huguet

“…This low-dimensional mean field model allows us to use tools from bifurcation theory to identify the phase-locked states between the input and the target population as a function of the amplitude, frequency and coherence of the inputs. …”
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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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