scholarly journals Existence and metastability of non-constant steady states in a Keller-Segel model with density-suppressed motility

2019 ◽  
Vol 1 (1) ◽  
pp. 1-15
Author(s):  
Peng Xia ◽  
Yazhou Han ◽  
Jicheng Tao ◽  
Manjun Ma
Keyword(s):  
Cell Proliferation ◽  
Bifurcation Analysis ◽  
Phase Plane ◽  
Analytical Approximation ◽  
Stationary Solutions ◽  
Steady States ◽  
Phase Plane Analysis ◽  
Plane Analysis ◽  
One Step ◽  
The One

We are concerned with stationary solutions of a Keller-SegelModel with density-suppressed motility and without cell proliferation. we establish the existence and the analytical approximation of non-constant stationary solutions by applying the phase plane analysis and bifurcation analysis. We show that the one-step solutions is stable and two or more-step solutions are always unstable. Then we further show that two or more-step solutions possess metastability. Our analytical results are corroborated by direct simulations of the underlying system.

Bifurcation analysis of the propagation of femtosecond pulses for the Triki-Biswas equation in monomode optical fibers

2019 ◽  
Vol 33 (29) ◽  
pp. 1950346 ◽  
Author(s):  
Asit Saha
Keyword(s):  
Optical Fibers ◽  
Bifurcation Analysis ◽  
Phase Plane ◽  
Dynamical Behavior ◽  
Phase Plane Analysis ◽  
Femtosecond Pulses ◽  
Plane Analysis ◽  
Solitary Pulse ◽  
Time Series Plot ◽  
First Time

Bifurcation analysis of the propagation of femtosecond pulses for the Triki–Biswas (TB) equation in monomode optical fibers is reported for the first time. Bifurcation of phase plots of the dynamical system is dispensed using phase plane analysis through symbolic computation. It is observed that the TB equation supports femtosecond solitary pulse, periodic pulse, superperiodic pulse, kink and anti-kink pulses, which are presented through time series plot numerically. Analytical forms of the femtosecond solitary pulses are obtained. This contribution may be applicable to interpret the dynamical behavior of various femtosecond pulses in monomode optical fibers beyond the Kerr limit.

scholarly journals DYNAMICAL EFFECTS FROM ASTEROID BELTS FOR PLANETARY SYSTEMS

2004 ◽  
Vol 14 (09) ◽  
pp. 3153-3166 ◽  
Author(s):  
ING-GUEY JIANG ◽  
LI-CHIN YEH
Keyword(s):  
Phase Plane ◽  
Kuiper Belt ◽  
Planetary Systems ◽  
Orbital Evolution ◽  
Outer Edge ◽  
Phase Plane Analysis ◽  
Keplerian Orbit ◽  
Plane Analysis ◽  
Natural Mechanism ◽  
The One

The orbital evolution and stability of planetary systems with interaction from the belts is studied using the standard phase-plane analysis. In addition to the fixed point which corresponds to the Keplerian orbit, there are other fixed points around the inner and outer edges of the belt. Our results show that for the planets, the probability to move stably around the inner edge is larger than the one to move around the outer edge. It is also interesting that there is a limit cycle of semi-attractor for a particular case. Applying our results to the Solar System, we find that our results could provide a natural mechanism to do the orbit rearrangement for the larger Kuiper Belt Objects and thus successfully explain the absence of these objects beyond 50 AU.

Phase-plane analysis of feedback control of unstable steady states in a biological reactor

AIChE Journal ◽  
1978 ◽  
Vol 24 (4) ◽  
pp. 686-693 ◽  
Author(s):  
David Dibiasio ◽  
Henry C. Lim ◽  
William A. Weigand ◽  
George T. Tsao
Keyword(s):  
Feedback Control ◽  
Phase Plane ◽  
Steady States ◽  
Phase Plane Analysis ◽  
Plane Analysis ◽  
Unstable Steady States

Whole-body phase plane analysis for standard maximum vertical jump assessment

2021 ◽  
Vol 90 ◽  
pp. 203-204
Author(s):  
C. Rodrigues ◽  
M. Correia ◽  
J. Abrantes ◽  
B. Rodrigues ◽  
J. Nadal
Keyword(s):  
Phase Plane ◽  
Vertical Jump ◽  
Whole Body ◽  
Phase Plane Analysis ◽  
Plane Analysis

scholarly journals Phase-plane analysis of driven multi-lane exclusion models

2012 ◽  
Vol 2012 (04) ◽  
pp. P04004 ◽  
Author(s):  
Vandana Yadav ◽  
Rajesh Singh ◽  
Sutapa Mukherji
Keyword(s):  
Phase Plane ◽  
Phase Plane Analysis ◽  
Plane Analysis

scholarly journals Subharmonic solutions of bounded coupled Hamiltonian systems with sublinear growth

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Fanfan Chen ◽  
Dingbian Qian ◽  
Xiying Sun ◽  
Yinyin Wu
Keyword(s):  
Hamiltonian Systems ◽  
Phase Plane ◽  
Phase Plane Analysis ◽  
Zero Eigenvalue ◽  
Subharmonic Solutions ◽  
Existence And Multiplicity ◽  
Plane Analysis ◽  
Higher Dimensional ◽  
Dimensional Version ◽  
Twist Theorem

<p style='text-indent:20px;'>We prove the existence and multiplicity of subharmonic solutions for bounded coupled Hamiltonian systems. The nonlinearities are assumed to satisfy Landesman-Lazer conditions at the zero eigenvalue, and to have some kind of sublinear behavior at infinity. The proof is based on phase plane analysis and a higher dimensional version of the Poincaré-Birkhoff twist theorem by Fonda and Ureña. The results obtained generalize the previous works for scalar second-order differential equations or relativistic equations to higher dimensional systems.</p>

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