Boundary equilibrium bifurcations in flows

2007 ◽  
pp. 219-252
Author(s):  
Mario di Bernardo ◽  
Alan R. Champneys ◽  
Christopher J. Budd ◽  
Piotr Kowalczyk
Keyword(s):  
Boundary Equilibrium

Two-Parameter Boundary Equilibrium Bifurcations in 3D-Filippov Systems

2019 ◽  
Vol 29 (6) ◽  
pp. 2845-2875 ◽  
Author(s):  
Rony Cristiano ◽  
Daniel J. Pagano
Keyword(s):  
Filippov Systems ◽  
Boundary Equilibrium ◽  
Two Parameter

scholarly journals Bifurcation Analysis in a Diffusive Mussel-Algae Model with Delay

2019 ◽  
Vol 29 (11) ◽  
pp. 1950144 ◽  
Author(s):  
Zuolin Shen ◽  
Junjie Wei
Keyword(s):  
Hopf Bifurcation ◽  
Functional Differential Equations ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Delayed Reaction ◽  
Center Manifold Reduction ◽  
Existence Of Positive Solutions ◽  
Boundary Equilibrium ◽  
Functional Differential ◽  
The Stability

In this paper, we consider the dynamics of a delayed reaction–diffusion mussel-algae system subject to Neumann boundary conditions. When the delay is zero, we show the existence of positive solutions and the global stability of the boundary equilibrium. When the delay is not zero, we obtain the stability of the positive constant steady state and the existence of Hopf bifurcation by analyzing the distribution of characteristic values. By using the theory of normal form and center manifold reduction for partial functional differential equations, we derive an algorithm that determines the direction of Hopf bifurcation and the stability of bifurcating periodic solutions. Finally, some numerical simulations are carried out to support our theoretical results.

Derivation of free-boundary equilibrium linear models by a flux perturbation method

2008 ◽  
Vol 49 (1) ◽  
pp. 015001
Author(s):  
P. Bettini ◽  
M. Cavinato ◽  
A. Portone
Keyword(s):  
Free Boundary ◽  
Perturbation Method ◽  
Linear Models ◽  
Boundary Equilibrium ◽  
Flux Perturbation

EFFECT OF SMALL BULK SULFUR CONTENT AND ANNEALING TEMPERATURE ON THE INTERGRANULAR FRACTURING SUSCEPTIBILITY OF METALLIC NICKEL

2016 ◽  
Vol 23 (06) ◽  
pp. 1650050 ◽  
Author(s):  
BOUTASSOUNA DJAMAL ◽  
RENÉ LE GALL ◽  
IBEN KHALDOUN LEFKAIER
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Sulfur Content ◽  
Auger Spectroscopy ◽  
Metallic Nickel ◽  
Boundary Equilibrium ◽  
Influence Of Temperature On ◽  
Sulfide Compound ◽  
Equilibrium Segregation

In this paper, we investigate the influence of temperature on the nickel grain boundary equilibrium segregation of sulfur and the resulting intergranular fracturing susceptibility. Auger electron spectroscopy has been used to study equilibrium segregation of sulfur to the grain boundaries of a metallic nickel, with a mass bulk content of 3.6[Formula: see text]ppm in sulfur. Samples were first annealed at adequate temperatures for sufficiently large equilibrium time, and then quenched in water at room temperature. The analysis carried out shows a significant increase of sulfur concentration in the grain boundary with decreasing temperature. However, the sulfur content in the grain boundary shows a drastic shrink at 700[Formula: see text]C. This can be interpreted by the formation of an aggregate sulfide compound in the area of the grain boundaries. At 650[Formula: see text]C, in situ brittle fracture becomes unworkable and only intragranular fractures are observed. Using the results obtained through the investigation of the grain boundaries by Auger spectroscopy, the standard segregation energy is estimated as [Formula: see text].

scholarly journals Global Stability and Optimal Control of Dengue with Two Coexisting Virus Serotypes

MATEMATIKA ◽  
2019 ◽  
Vol 35 (4) ◽  
pp. 149-170
Author(s):  
Afeez Abidemi ◽  
Rohanin Ahmad ◽  
Nur Arina Bazilah Aziz
Keyword(s):  
Optimal Control ◽  
Global Stability ◽  
Disease Transmission ◽  
Deterministic Model ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Effective Control ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Boundary Equilibrium

This study presents a two-strain deterministic model which incorporates Dengvaxia vaccine and insecticide (adulticide) control strategies to forecast the dynamics of transmission and control of dengue in Madeira Island if there is a new outbreak with a different virus serotypes after the first outbreak in 2012. We construct suitable Lyapunov functions to investigate the global stability of the disease-free and boundary equilibrium points. Qualitative analysis of the model which incorporates time-varying controls with the specific goal of minimizing dengue disease transmission and the costs related to the control implementation by employing the optimal control theory is carried out. Three strategies, namely the use of Dengvaxia vaccine only, application of adulticide only, and the combination of Dengvaxia vaccine and adulticide are considered for the controls implementation. The necessary conditions are derived for the optimal control of dengue. We examine the impacts of the control strategies on the dynamics of infected humans and mosquito population by simulating the optimality system. The disease-freeequilibrium is found to be globally asymptotically stable whenever the basic reproduction numbers associated with virus serotypes 1 and j (j 2 {2, 3, 4}), respectively, satisfy R01,R0j 1, and the boundary equilibrium is globally asymptotically stable when the related R0i (i = 1, j) is above one. It is shown that the strategy based on the combination of Dengvaxia vaccine and adulticide helps in an effective control of dengue spread in the Island.

Bursting Oscillations as well as the Mechanism in a Filippov System with Parametric and External Excitations

2020 ◽  
Vol 30 (12) ◽  
pp. 2050168
Author(s):  
Hongfang Han ◽  
Qinsheng Bi
Keyword(s):  
Autonomous System ◽  
Type System ◽  
External Excitation ◽  
Nonsmooth Boundary ◽  
Bursting Oscillations ◽  
Fold Bifurcation ◽  
Different Types ◽  
Boundary Equilibrium ◽  
Parametric And External Excitations ◽  
Filippov Type

The main purpose of this paper is to explore the bursting oscillations as well as the mechanism of a parametric and external excitation Filippov type system (PEEFS), in which different types of bursting oscillations such as fold/nonsmooth fold (NSF)/fold/NSF, fold/NSF/fold and fold/fold bursting oscillations can be observed. By employing the overlap of the transformed phase portrait and the equilibrium branches of the generalized autonomous system, the mechanisms of the bursting oscillations are investigated. Our results show that the fold bifurcation and the boundary equilibrium bifurcation (BEB) can cause the transitions between the quiescent states and repetitive spiking states. The oscillating frequencies of the spiking states can be approximated theoretically by their occurring mechanisms, which agree well with the numerical simulations. Furthermore, some nonsmooth evolutions are investigated by employing differential inclusions theory, which reveals that the positional relationship between the points of the trajectory interacting with the nonsmooth boundary and the related sliding boundary of the nonsmooth system may affect the nonsmooth evolutions.

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