scholarly journals On global bifurcation for the nonlinear Steklov problems

2021 ◽  
pp. 1-33
Author(s):  
Thazhe Veetil Anoop ◽  
Nirjan Biswas
Keyword(s):  
Global Bifurcation

scholarly journals The influence of density in population dynamics with strong and weak Allee effect

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Kamrun Nahar Keya ◽  
Md. Kamrujjaman ◽  
Md. Shafiqul Islam
Keyword(s):  
Population Dynamics ◽  
Allee Effect ◽  
Global Bifurcation ◽  
Reaction Diffusion ◽  
Logistic Growth ◽  
Allee Effects ◽  
Reaction Diffusion Model ◽  
Positive Steady States ◽  
The Stability ◽  
The Impact

AbstractIn this paper, we consider a reaction–diffusion model in population dynamics and study the impact of different types of Allee effects with logistic growth in the heterogeneous closed region. For strong Allee effects, usually, species unconditionally die out and an extinction-survival situation occurs when the effect is weak according to the resource and sparse functions. In particular, we study the impact of the multiplicative Allee effect in classical diffusion when the sparsity is either positive or negative. Negative sparsity implies a weak Allee effect, and the population survives in some domain and diverges otherwise. Positive sparsity gives a strong Allee effect, and the population extinct without any condition. The influence of Allee effects on the existence and persistence of positive steady states as well as global bifurcation diagrams is presented. The method of sub-super solutions is used for analyzing equations. The stability conditions and the region of positive solutions (multiple solutions may exist) are presented. When the diffusion is absent, we consider the model with and without harvesting, which are initial value problems (IVPs) and study the local stability analysis and present bifurcation analysis. We present a number of numerical examples to verify analytical results.

scholarly journals The existence of positive solutions for Kirchhoff-type problems via the sub-supersolution method

2018 ◽  
Vol 26 (1) ◽  
pp. 5-41 ◽  
Author(s):  
Baoqiang Yan ◽  
Donal O’Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Positive Solutions ◽  
Bifurcation Theory ◽  
Sufficient Conditions ◽  
Global Bifurcation ◽  
Existence Of A Solution ◽  
Kirchhoff Type ◽  
Existence Of Positive Solutions ◽  
Global Bifurcation Theory ◽  
Necessary And Sufficient ◽  
Kirchhoff Type Problems

Abstract In this paper we discuss the existence of a solution between wellordered subsolution and supersolution of the Kirchhoff equation. Using the sub-supersolution method together with a Rabinowitz-type global bifurcation theory, we establish the existence of positive solutions for Kirchhoff-type problems when the nonlinearity is singular or sign-changing. Moreover, we obtain some necessary and sufficient conditions for the existence of positive solutions for the problem when N = 1.

Global bifurcation for nonlinear equations

2008 ◽  
Vol 69 (8) ◽  
pp. 2362-2368 ◽  
Author(s):  
In-Sook Kim ◽  
Yun-Ho Kim
Keyword(s):  
Nonlinear Equations ◽  
Global Bifurcation

scholarly journals A New Approach of Asymmetric Homoclinic and Heteroclinic Orbits Construction in Several Typical Systems Based on the Undetermined Padé Approximation Method

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Jingjing Feng ◽  
Qichang Zhang ◽  
Wei Wang ◽  
Shuying Hao
Keyword(s):  
Dynamic Systems ◽  
Approximation Method ◽  
Padé Approximation ◽  
Global Bifurcation ◽  
Heteroclinic Orbits ◽  
Symmetric System ◽  
Pade Approximation ◽  
New Approach ◽  
Homoclinic And Heteroclinic Orbits ◽  
Single Orbit

In dynamic systems, some nonlinearities generate special connection problems of non-Z2symmetric homoclinic and heteroclinic orbits. Such orbits are important for analyzing problems of global bifurcation and chaos. In this paper, a general analytical method, based on the undetermined Padé approximation method, is proposed to construct non-Z2symmetric homoclinic and heteroclinic orbits which are affected by nonlinearity factors. Geometric and symmetrical characteristics of non-Z2heteroclinic orbits are analyzed in detail. An undetermined frequency coefficient and a corresponding new analytic expression are introduced to improve the accuracy of the orbit trajectory. The proposed method shows high precision results for the Nagumo system (one single orbit); general types of non-Z2symmetric nonlinear quintic systems (orbit with one cusp); and Z2symmetric system with high-order nonlinear terms (orbit with two cusps). Finally, numerical simulations are used to verify the techniques and demonstrate the enhanced efficiency and precision of the proposed method.

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