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.…”

A simplified model of the Martian atmosphere - Part 2: a POD-Galerkin analysis by Whitehouse, S, Lewis, SR, 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. © 2005 Author(s). …”

DROP TAIL AND RED QUEUE MANAGEMENT WITH SMALL BUFFERS:STABILITY AND HOPF BIFURCATION by Ganesh Patil, Sally McClean, Gaurav Raina3

“…For Drop Tail, the analytical arguments are based on local stability and bifurcation theory. As the buffer size acts as a bifurcation parameter, variations in it can readily lead to the emergence of limit cycles. …”
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Existence and stability of traveling waves in parabolic systems of differential equations with weak diffusion by I.I. Klevchuk

“…We use the normal forms method in the general parabolic system of differential equations with retarded argument and weak diffusion. We use bifurcation theory for delay differential equations and quasilinear parabolic equations. …”
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Global Bifurcation Behaviors and Control in a Class of Bilateral MEMS Resonators by Yijun Zhu, Huilin Shang

“…The results may have some potential value in broadening the application fields of global bifurcation theory and improving the performance reliability of capacitive MEMS devices.…”
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Bifurcation and complex dynamics of a discrete-time predator-prey system by S. M. Sohel Rana

“…It is shown that the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation in the interior of R+2 by using bifurcation theory. It has been found that the dynamical behavior of the model is very sensitive to the parameter values and the initial conditions. …”
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Spatiotemporal Tipping Induced by Turing Instability and Hopf Bifurcation in a Population Ecosystem Model with the Fear Factor by Min Xiao, Gong Chen, Feilong Wang, Zunshui Cheng, Yi Yao

“…Using techniques from bifurcation theory, we can predict the emergence of tipping points based on a spatiotemporal predator-prey system having a fear effect before an instability is encountered. …”
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Bifurcation studies, chaotic pattern, phase diagrams and multiple optical solitons for the (2+1)-dimensional stochastic coupled nonlinear Schrödinger system with multiplicative whi... by Lu Tang

“…Here, we analytically deduced bright solitons, dark solitons and periodic solutions through the bifurcation theory. Additionally, some other bounded traveling wave solutions which include Jacobi elliptic function solutions, trigonometric function solutions, rational function solutions, hyperbolic function solutions and solitary wave solutions are also obtained by using the symbolic computation as well as the complete discriminant system method. …”
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XOR Multiplexing Technique for Nanocomputers by Lianhua Yu, Ming Diao, Xiaobo Chen, Xiaochun Cheng

“…The simulation results show that XOR multiplexing is more reliable than NAND multiplexing. Bifurcation theory is used to analyze the fault-tolerant ability of the system and the results show that XOR multiplexing technique has a high fault-tolerant ability. …”
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Data-driven detection of critical points of phase transitions in complex systems by Peng Tao, Chenghang Du, Yi Xiao, Chen Zeng

“…In these regards, the dynamic network biomarker/marker (DNB) method derived from the bifurcation theory is currently very popular, but a unified criterion to pick the most appropriate DNBs is lacking. …”
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Discretization, Bifurcation, and Control for a Class of Predator-Prey Interactions by Asifa Tassaddiq, Muhammad Sajjad Shabbir, Qamar Din, Humera Naaz

“…By implementing the center manifold theorem and bifurcation theory, our study reveals that the given system undergoes period-doubling and Neimark-Sacker bifurcation around the interior equilibrium point. …”
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Chaotic dynamics of the fractional order Schnakenberg model and its control by Md. Jasim Uddin, S. M. Sohel Rana

“…Using central manifold and bifurcation theory, we demonstrate the presence and direction of NS and Flip bifurcations. …”
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Bifurcation analysis of a three dimensional system by Yongwen WANG, Zhiqin QIAO, Yakui XUE

“…In order to enrich the stability and bifurcation theory of the three dimensional chaotic systems, taking a quadratic truncate unfolding system with the triple singularity equilibrium as the research subject, the existence of the equilibrium, the stability and the bifurcation of the system near the equilibrium under different parametric conditions are studied. …”
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Hyperbolic planforms in relation to visual edges and textures perception. by Pascal Chossat, Olivier Faugeras

“…We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. …”
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The Qualitative Analysis of Host–Parasitoid Model with Inclusion of Spatial Refuge Effect by Muhammad Sajjad Shabbir, Qamar Din, Wafa F. Alfwzan, Manuel De la Sen

“…A local stability analysis of host–parasitoid models was also carried out. Bifurcation theory was used to observe that the host–parasitoid models undergo Neimark–Sacker bifurcation. …”
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Orbital Stability and Invariant Manifolds on Distant Retrograde Orbits around Ganymede and Nearby Higher-Period Orbits by Qingqing Li, Yuming Tao, Fanghua Jiang

“…In particular, the DRO family is calculated by numerical integration and numerical continuation, higher-period orbits near the DROs are detected using bifurcation theory, and characteristics including orbital stability and invariant manifolds of these orbits are investigated through stability indices and manifold theory. …”
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Multi-scale dynamics of predator-prey systems with Holling-IV functional response by Kexin Zhang, Caihui Yu, Hongbin Wang, Xianghong Li

“…This study aims to address how the slowly varying environmental capacity parameter affects the behavior of the system. Based on bifurcation theory and the slow-fast analysis method, the critical condition for the Hopf bifurcation of the autonomous system is given. …”
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Complex dynamics and control of a novel physical model using nonlocal fractional differential operator with singular kernel by A.E. Matouk, I. Khan

“…Conditions for the approximating periodic solution in this model via Hopf bifurcation theory are discussed. Chaotic dynamics are found in the commensurate system for a wide range of fractional orders. …”
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Synchronization degree of a two-compartment neuron based on transcranial magnetic stimulation by Pu Chen, Quan Yuan

“…We are established the correlation degree with synchronization, and discussed the firing mode and transition rule of the neurons in the two-compartment compartment pre-Bötzinger complex (PBC) by means of bifurcation theory and Lyapunov index. The results show that the synchronization of neurons has a great influence under TMS, which is embodied in the fact that the somatic will experience a peak firing and a transition from bursting to resting under the magnetic stimulation,which was a phenomenon never before shown in PBC neurons. …”
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Bistability by multiple phosphorylation of regulatory proteins. by Kapuy, O, Barik, D, Sananes, MR, Tyson, J, Novák, B

“…Using numerical simulations and bifurcation theory, we study the properties of a particular bistable reaction network motivated by the antagonistic relationship between cyclin-dependent kinase and its multiply phosphorylated target, Cdh1, which is involved in the degradation of cyclin molecules. …”