Firing patterns and bifurcation analysis of Purkinje cell dendrite model

2022 ◽  
Author(s):  
Xiaoshan Huang ◽  
Shenquan Liu ◽  
Pan Meng ◽  
Jie Zang
Keyword(s):  
Purkinje Cell ◽  
Bifurcation Analysis ◽  
Phase Plane Analysis ◽  
Cell Dendrite ◽  
Theoretical Derivation ◽  
Firing Patterns ◽  
Plane Analysis ◽  
Purkinje Cell Dendrite ◽  
Lyapunov Coefficient ◽  
The Stability

This paper mainly studied firing patterns and related bifurcations in the Purkinje cell dendrite model. Based on the methods of equivalent potentials and time scale analysis, the initial six-dimensional (6D) dendrite model is reduced to a 3D form to facilitate the calculation. We numerically show that the dendrite model could exhibit period-adding bifurcation and four bursting patterns for several vital parameters. Then the bifurcation mechanisms and transition of these four bursting patterns are discussed by phase plane analysis, and two-parameter bifurcation analysis of the fast subsystem, respectively. Moreover, we computed the first Lyapunov coefficient to determine the stability of Hopf bifurcation. Ultimately, we analyzed the codimension-two bifurcation of the whole system and gave a detailed theoretical derivation of the Bogdanov–Takens bifurcation.

scholarly journals P-Rex2 regulates Purkinje cell dendrite morphology and motor coordination

2008 ◽  
Vol 105 (11) ◽  
pp. 4483-4488 ◽  
Author(s):  
S. Donald ◽  
T. Humby ◽  
I. Fyfe ◽  
A. Segonds-Pichon ◽  
S. A. Walker ◽  
...  
Keyword(s):  
Purkinje Cell ◽  
Motor Coordination ◽  
Cell Dendrite ◽  
Dendrite Morphology ◽  
Purkinje Cell Dendrite

scholarly journals THE DYNAMICS OF TACHYON FIELD WITH AN INVERSE SQUARE POTENTIAL IN LOOP QUANTUM COSMOLOGY

2013 ◽  
Vol 22 (06) ◽  
pp. 1350030 ◽  
Author(s):  
FEI HUANG ◽  
JIAN-YANG ZHU ◽  
KUI XIAO
Keyword(s):  
Quantum Cosmology ◽  
Dynamical Behavior ◽  
Loop Quantum Cosmology ◽  
Phase Plane Analysis ◽  
Late Time ◽  
Stable Node ◽  
Time Behavior ◽  
Tachyon Field ◽  
Plane Analysis ◽  
The Stability

The dynamical behavior of tachyon field with an inverse potential is investigated in loop quantum cosmology. It reveals that the late-time behavior of tachyon field with this potential leads to a power-law expansion. In addition, an additional barotropic perfect fluid with the adiabatic index 0 < γ < 2 is added and the dynamical system is shown to be an autonomous one. The stability of this autonomous system is discussed using phase plane analysis. There exist up to five fixed points with only two of them possibly stable. The two stable node (attractor) solutions are specified and their cosmological indications are discussed. For the tachyon dominated solution, the further discussion is stretched to the possibility of considering tachyon field as a combination of two parts which respectively behave like dark matter and dark energy.

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 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.

scholarly journals INDUCED PHANTOM AND 5D ATTRACTOR SOLUTION IN SPACETIME–MATTER THEORY

2005 ◽  
Vol 20 (26) ◽  
pp. 1973-1981 ◽  
Author(s):  
HONGYA LIU ◽  
HUANYING LIU ◽  
BAORONG CHANG ◽  
LIXIN XU
Keyword(s):  
Phase Plane ◽  
Phase Plane Analysis ◽  
Late Time ◽  
Plane Analysis ◽  
Spacetime Singularity ◽  
Attractor Solution ◽  
Matter Theory ◽  
Cosmological Solutions ◽  
The Stability ◽  
Induced Matter

In Spacetime–Matter theory we assume that the 4D induced matter of the 5D Ricci-flat bouncing cosmological solutions contains a perfect fluid as well as an induced scalar field. Then we show that the conventional 4D quintessence and phantom models of dark energy could be recovered from the 5D cosmological solutions. By using the phase-plane analysis to study the stability of evolution of the 5D models, we find that the conventional 4D late-time attractor solution is also recovered. This attractor solution shows that the scale factors of the phantom dominated universes in both the 4D and 5D theories will reach infinity in a finite time and the universes will be ended at a new kind of spacetime singularity at which everything will be annihilated. We also find that the repulsive force of the phantom may provide us with a mechanics to explain the bounce.

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