The analysis of dynamic of chemical reaction networks by computing Hopf bifurcation is a method to understand the qualitative behavior of the network due to its relation to the existence of oscillations. For low dimensional reaction systems without additional constraints Hopf bifurcation can be computed by reducing the question of its occurrence to quantifier elimination problems on real closed...

Robustness is an essential feature of biological systems, and any mathematical model that describes such a system should reflect this feature. Especially, persistence of oscillatory behavior is an important issue. A benchmark model for this phenomenon is the Laub-Loomis model, a nonlinear model for cAMP oscillations in Dictyostelium discoideum. This model captures the most important features of...

We consider a family of one-dimensional continuous piecewise smooth maps with monotone increasing and monotone decreasing branches. It is associated with a credit cycle model introduced by Matsuyama, under the assumption of the Cobb-Douglas production function. We offer a detailed analysis of the dynamics of this family. In particular, using the skew tent map as a border collision normal form w...

A general process of the immune system consists of effector stage and memory stage. Current theoretical studies of the immune system often focus on the memory stage and pay less attention on the function of non-immune system substances such as tissue cells in adjusting the dynamical behavior of the immune system. We propose a mathematical population model to investigate the interaction between ...

In this survey we report on some recent results related to various singular phenomena arising in the study of some classes of nonlinear elliptic equations. We establish qualitative results on the existence, nonexistence or the uniqueness of solutions and we focus on the following types of problems: (i) blow-up boundary solutions of logistic equations; (ii) Lane-Emden-Fowler equations with singu...

In this paper, the stability analysis of an anaerobic digestion process is presented. The analysis is performed using a simplified mathematical model, which includes explicit temperature and pH dependence on kinetic growth rates. A detailed nonlinear and bifurcation analyses are performed in order to study the effects of temperature and pH parameters on the process behaviour. In addition, both ...

Systems that are spatially coupled generally shows complicated spatially and temporally turbulent states. The coupled magneto-elastic beam system is an experimental model which has an elastically continuous and magnetically discrete structure. In this Letter, quasi-periodic wave and its bifurcation in the coupled system are numerically discussed.  2001 Elsevier Science B.V. All rights reserved...

The aim of this paper is to investigate the bifurcation and chaotic behaviour in the two-parameter family of transcendental functions fλ,n(x) = λ x (ex+1)n , λ > 0, x ∈ R, n ∈ N\{1} which arises from the generating function of the generalized Apostol-type polynomials. The existence of the real fixed points of fλ,n(x) and their stability are studied analytically and the periodic points of fλ,n(x...

In this note, we study the existence and multiplicity of solutions, strictly positive or nonnegative having a dead core (where the solution vanishes) of several nonlinear problems of eigenvalue type. 2000 Mathematics Subject Classification: 35J60, 35B52.

A mathematical model for the quantitative analysis of cancer immune interaction, considering the role of antibodies has been proposed in this paper. The model is based on the clinical evidence, which states that antibodies can directly kill cancerous cells [1]. The existence of transcritical and saddle-node bifurcation, which has been proved using Sotomayor theorem, provides strong biological i...