Bifurcation analysis and approximate analytical periodic solution of ER3BP with radiation and albedo effects

2021 ◽  
Vol 366 (3) ◽  
Author(s):  
Ruifang Wang ◽  
Yongqing Wang ◽  
Fabao Gao
Keyword(s):  
Periodic Solution ◽  
Bifurcation Analysis

Calculation of the Periodic Solution in Nakamura’s Model

2012 ◽  
Vol 256-259 ◽  
pp. 1648-1651
Author(s):  
Bin Zhen ◽  
Zhang Jun Liu
Keyword(s):  
Periodic Solution ◽  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Bifurcation Analysis ◽  
Energy Method ◽  
Analytic Solution ◽  
Measure Data ◽  
Lateral Vibration ◽  
Lateral Vibrations

Nakamura’s model is one of the most practical models describing the lateral vibrations of footbridges induced by pedestrians. This paper presents a calculation of the periodic solution in Nakamura’s model. After a Hopf bifurcation analysis of Nakamura’s model, the amplitude of the lateral vibration is computed by using the energy method. The correctness and accuracy of the calculation is demonstrated by numerical simulations. Then, how the factors and variables in Nakamura’s model effect the amplitude is investigated based on the analytic solution. Our analysis results may be used to explain why the most of the predict results of Nakamura’s model are larger than the measure data.

scholarly journals Hopf Bifurcation Analysis for a Two Species Periodic Chemostat Model with Discrete Delays

2020 ◽  
pp. 93-105
Author(s):  
Jane Ireri ◽  
Ganesh Pokhariyal ◽  
Stephene Moindi
Keyword(s):  
Periodic Solution ◽  
Fourier Series ◽  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Nutrient Input ◽  
Chemostat Model ◽  
Bifurcation Theorem ◽  
Interior Equilibrium ◽  
Limiting Nutrient ◽  
Discrete Delays

In this paper we analyze a Chemostat model of two species competing for a single limiting nutrient input varied periodically using a Fourier series with discrete delays. To understand global aspects of the dynamics we use an extension of the Hopf bifurcation theorem, a method that rigorously establishes existence of a periodic solution. We show that the interior equilibrium point changes its stability and due to the delay parameter it undergoes a Hopf bifurcation.Numerical results shows that coexistence is possible when delays are introduced and Fourier series produces the required seasonal variations. We also show that for small delays periodic variations of nutrients has more influence on species density variations than the delay.

BIFURCATION ANALYSIS OF THE PROPAGATING WAVE AND THE SWITCHING SOLUTIONS IN A RING OF SIX-COUPLED BISTABLE OSCILLATORS — BIFURCATION STARTING FROM TYPE 2 STANDING WAVE SOLUTION

2012 ◽  
Vol 22 (05) ◽  
pp. 1250123 ◽  
Author(s):  
KYOHEI KAMIYAMA ◽  
MOTOMASA KOMURO ◽  
TETSURO ENDO
Keyword(s):  
Periodic Solution ◽  
Standing Wave ◽  
Bifurcation Analysis ◽  
Coupling Strength ◽  
Wave Solution ◽  
Pitchfork Bifurcation

In this paper, we analyze the bifurcation of Type 2 periodic solution in a ring of six-coupled bistable oscillators. We show that pitchfork and heteroclinic bifurcations, which induce chaos, cause a change from periodic (standing wave) solution to quasi-periodic (propagating wave) solution or the inverse when the coupling strength is varied. We also explain the existence of the switching solution, and presume that the birth and death of this switching solution are due to a pitchfork bifurcation of a quasi-periodic solution.

scholarly journals Bifurcation Analysis of a Chemostat Model of Plasmid-Bearing and Plasmid-Free Competition with Pulsed Input

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Zhong Zhao ◽  
Baozhen Wang ◽  
Liuyong Pang ◽  
Ying Chen
Keyword(s):  
Periodic Solution ◽  
Bifurcation Analysis ◽  
Bifurcation Theory ◽  
Chemostat Model ◽  
Periodic Oscillations ◽  
Free Competition ◽  
The Stability ◽  
Invasion Threshold ◽  
Standard Techniques

A chemostat model of plasmid-bearing and plasmid-free competition with pulsed input is proposed. The invasion threshold of the plasmid-bearing and plasmid-free organisms is obtained according to the stability of the boundary periodic solution. By use of standard techniques of bifurcation theory, the periodic oscillations in substrate, plasmid-bearing, and plasmid-free organisms are shown when some conditions are satisfied. Our results can be applied to control bioreactor aimed at producing commercial producers through genetically altered organisms.

Hopf bifurcation analysis of predator–prey model with two delays and disease transmission

2020 ◽  
Vol 13 (07) ◽  
pp. 2050068
Author(s):  
Renxiang Shi
Keyword(s):  
Periodic Solution ◽  
Hopf Bifurcation ◽  
Global Existence ◽  
Bifurcation Analysis ◽  
Disease Transmission ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Two Delays

In this paper, we study the Hopf bifurcation of predator–prey system with two delays and disease transmission. Furthermore, the global existence of bifurcated periodic solution was studied, the influence of disease transmission is given. At last, some simulations are given to support our result.

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

Sign in / Sign up

Export Citation Format

Share Document