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The Transcritical Bogdanov-Takens Bifurcation with Boundary Due to Risk Perception in an Epidemiological Model

Jocelyn Anaid Castro Echeverría, Fernando Verduzco, Jorge X. Velasco‐Hernández   +2 more
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Emergence failure of early epidemics: A mathematical modeling approach. [PDF]

PLoS One
Breban R.
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Revealing unseen dynamical regimes of ecosystems from population time-series data. [PDF]

Proc Natl Acad Sci U S A
Medeiros LP, Sorenson DK, Johnson BJ, Palkovacs EP, Munch SB.   +4 more
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Seasonal refuge patterns of phytoplankton trigger irregular bloom events in a contaminated environment. [PDF]

Sci Rep
Mandal A, Biswas S, Tiwari PK, Pal S.
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BIFURCATIONS OF GENERIC HETEROCLINIC LOOP ACCOMPANIED BY TRANSCRITICAL BIFURCATION

International Journal of Bifurcation and Chaos, 2008
The bifurcations of generic heteroclinic loop with one nonhyperbolic equilibrium p1and one hyperbolic saddle p2are investigated, where p1is assumed to undergo transcritical bifurcation. Firstly, we discuss bifurcations of heteroclinic loop when transcritical bifurcation does not happen, the persistence of heteroclinic loop, the existence of homoclinic ...
Geng, Fengjie, Liu, Dan, Zhu, Deming
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Solution and transcritical bifurcation of Burgers equation

Chinese Physics B, 2011
Burgers equation is reduced into a first-order ordinary differential equation by using travelling wave transformation and it has typical bifurcation characteristics. We can obtain many exact solutions of the Burgers equation, discuss its transcritical bifurcation and control dynamical behaviours by extending the stable region.
Jia-Shi Tang, Ming-Hua Zhao, Feng Han, Liang Zhang   +3 more
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Hopf-transcritical bifurcation in retarded functional differential equations

Nonlinear Analysis: Theory, Methods & Applications, 2010
Firstly, a codimension-two unfolding for the Hopf-transcritical bifurcation is studied, and complete bifurcation diagrams and phase portraits are given. In particular, the heteroclinic bifurcation curve is investigated explicitly, and conditions are obtained under which the secondary bifurcation periodic solutions and the heteroclinic orbit are stable.
Jiang, Weihua, Wang, Hongbin
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Homoclinic flip bifurcations accompanied by transcritical bifurcation

Chinese Annals of Mathematics, Series B, 2011
The author investigates the bifurcation of a homoclinic loop with a nonhyperbolic equilibrium by constructing a suitable Poincaré map. Using the fundamental solutions to linear variational equations as an active coordinate system, he constructs a global map which is composed of a regular map in the tubular neighborhood of the homoclinic orbit and a ...
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The transcritical bifurcation in absolutely stable feedback systems

2009 European Control Conference (ECC), 2009
The paper gives new conditions for the occurrence of a transcritical bifurcation in a non-negative passive system under non-linear static feedback. In biological systems, this provides a mechanism for defining activation thresholds in positive feedback systems.
Matthias A. Muller, Steffen Waldherr, Frank Allgower   +2 more
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