Differential Equations and Dynamical Systems

article

Almost periodic solutions of a functional differential equation by monotone iterative method

S. Abbas, D. Bahuguna

Differential Equations and Dynamical Systems > 2008 > 16 > 1-2 > 47-62

In this paper we show the existence of a maximal and a minimal almost periodic solution of a non-autonomous functional differential equation using the method of lower and upper solutions.

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Hopf bifurcation and periodic solutions in a dynamical model for HIV and immune response

P. K. Srivastava, Peeyush Chandra

Differential Equations and Dynamical Systems > 2008 > 16 > 1-2 > 77-100

A mathematical model for the effect of immune response on the dynamics of HIV is considered and analyzed. Further, delay in the activation of CTLs (Cytotoxic T Lymphocytes) is accounted in model and existence of the Hopf bifurcation and periodic solutions is investigated by considering delay as parameter. The direction, stability and period of the bifurcating periodic solutions are found explicitly.

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Dynamics in numerics: On a discrete predator-prey model

Yu Huang, Xiamei Jiang, Xingfu Zou

Differential Equations and Dynamical Systems > 2008 > 16 > 1-2 > 163-182

In this paper, we consider the dynamics of a discrete predator-prey model which is a result of discretization of the corresponding continuous Lotka-Volterra predator-prey model. Among the topis are equilibria and their stability, existence and stability of a period-2 orbit, as well the chaotic behavior of F. The chaos here is in the sense of topological horseshoe and is obtained for certain range...

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Existence and multiplicity of positive and negative solutions for higher-order multi-point Sturm-Liouville boundary value problems

Alex P. Palamides

Differential Equations and Dynamical Systems > 2008 > 16 > 1-2 > 121-143

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Multiple positive solutions for nonlinear third order general three-point boundary value problems

K. R. Prasad, P. Murali

Differential Equations and Dynamical Systems > 2008 > 16 > 1-2 > 63-75

We consider the third order nonlinear three point boundary value problem, $$ y'''(t) + f(t,y(t)) = 0,t \in [t_1 ,t_3 ], $$ subject to the general boundary conditions $$ \sum\limits_{j = 1}^3 {\alpha _{ij} y^{(j - 1)} (t_i ) = 0,i = 1,2,3,} $$ where f: [t ₁, t ₃] × IR → IR is continuous, t ₁ < t ₂ < t ₃ and α _i1, α _i2, α _i3, i = 1, 2, 3, are real constants. We establish the existence...

article

Editorial

V. Sree Hari Rao, Xingfu Zou

Differential Equations and Dynamical Systems > 2008 > 16 > 1-2 > 1-2

article

Korteweg-de Vries-Burgers equation with a higher-order nonlinearity

Zhaosheng Feng, Indranil Sen Gupta

Differential Equations and Dynamical Systems > 2008 > 16 > 1-2 > 3-27

In this paper, we study a Korteweg-de Vries-Burgers equation with a higher-order nonlinearity. An asymptotic analysis of proper traveling wave solutions is presented by means of the qualitative theory of differential equations. An approximate solution with arbitrary velocity is obtained by using the Adomian decomposition method, which agrees well with the phase plane analysis. A class of solitary...

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Dynamical models for the development of unilingual society into bilingual society

V. Sree Hari Rao, P. Raja Sekhara Rao

Differential Equations and Dynamical Systems > 2008 > 16 > 1-2 > 29-45

In this article, we present a mathematical model of a unilingual society developing in to a bilingual society. We formulate, analyze the model and interpret the results of the analysis. The model is based on a two language policy motivated by the cultural and historical back ground of India.

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Bifurcation analysis in an age-structured model of single species living in two identical patches

Aying Wan, Chunbo Yu

Differential Equations and Dynamical Systems > 2008 > 16 > 1-2 > 101-120

This paper deals with the age-structured model of a single species living in two identical pathes proposed in [12]. The dynamics of this model is still largely undetermined, and in this paper, we perform some bifurcation analysis to the model. By combining the normal form method with the center manifold theorem, we are able to determine the Hopf bifurcation properties. Finally, some numerical simulations...

article

Stochastic dynamics and passage times for diffusion approximations

P. R. Vittal, T. Jagadesan, V. Muralidhar

Differential Equations and Dynamical Systems > 2008 > 16 > 1-2 > 145-161

We discuss first passage time problems for a class of one dimensional master equations with separable kernels. For this class of master equations, the integral equations for first passage time moments (FPTM) have been transformed exactly into ordinary differential equations by Weiss and Szabo. There the boundary conditions for the first passage time moments have been introduced separately. In our...

article

Oscillation of mixed neutral functional differential equations with distributed deviating arguments

T. Candan, R. S. Dahiya

Differential Equations and Dynamical Systems > 2008 > 16 > 3 > 207-223

In this paper, we shall consider mixed neutral functional differential equations. New results on sufficient conditions for the oscillation behavior of solutions for this functional differential equation are presented. Few applications of these theorems obtained are also presented.

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Mathematical analysis of the role of repeated exposure on malaria transmission dynamics

Ashrafi M. Niger, Abba B. Gumel

Differential Equations and Dynamical Systems > 2008 > 16 > 3 > 251-287

This paper presents a deterministic model for assessing the role of repeated exposure on the transmission dynamics of malaria in a human population. Rigorous qualitative analysis of the model, which incorporates three immunity stages, reveals the presence of the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated...

article

Effect of small time delay in a predator-prey model within random environment

Tapan Saha, M. Banerjee

Differential Equations and Dynamical Systems > 2008 > 16 > 3 > 225-250

We consider a non-Kolmogorov type predator-prey model with and without delay. The local stability and Hopf bifurcation results are stated for both the cases of the deterministic system. The effect of stochastic perturbation in the form of parametric white and colored noise are considered. The exponential mean square stability of the trivial solutions for the stochastic differential equations and stochastic...

article

Almost periodic solutions of nonlinear functional differential equations

S. Abbas, D. Bahuguna

Differential Equations and Dynamical Systems > 2008 > 16 > 3 > 289-308

In this paper the existence of almost periodic solutions to a non-autonomous functional differential equation in a complex Banach space has been discussed using the semigroup theory of evolution equations and fixed point theorem.

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Stability of the second order delay differential equations with a damping term

Leonid Berezansky, Elena Braverman, Alexander Domoshnitsky

Differential Equations and Dynamical Systems > 2008 > 16 > 3 > 185-205

For the delay differential equations $$ \ddot x(t) + a(t)\dot x(g(t)) + b(t)x(h(t)) = 0,g(t) \leqslant t,h(t) \leqslant t, $$ and $$ \ddot x(t) + a(t)\dot x(t) + b(t)x(t) + a_1 (t)\dot x(g(t)) + b_1 (t)x(h(t)) = 0 $$ explicit exponential stability conditions are obtained.

article

On bifurcation and chaos in a discrete dynamical system

R. P. Pant

Differential Equations and Dynamical Systems > 2008 > 16 > 4 > 333-350

The aim of the present paper is to define a class of nonlinear functions on the set of non-negative real numbers and study the dynamics and periodic points of these functions. We show that this class of functions contains chaotic functions and exhibits the phenomenon of bifurcation. We also apply the results on dynamics of these functions to obtain general tests of divisibility of numbers and conditions...

article

A Kolmogorov-Fokker-Planck approach for a stochastic Duffing-van der Pol system

Shambhu N. Sharma

Differential Equations and Dynamical Systems > 2008 > 16 > 4 > 351-377

The stochastic Duffing-van der Pol (SDvdP) system is an appealing case in stochastic system theory, since it involves linear and non-linear vector fields, i.e. system non-linearities, state-independent and state-dependent stochastic accelerations. The equation describing the Duffing-van der Pol system is a second-order non-linear autonomous differential equation. Stochastic estimation procedures,...

article

Existence for the thermoviscoelastic thermistor problem

K. L. Kuttler, M. Shillor, J. R. Fernández

Differential Equations and Dynamical Systems > 2008 > 16 > 4 > 309-332

The existence of a weak solution to a dynamic model for a thermistor, which takes into account the thermoelastic properties of the device, is established. The model consists of a coupled system of the equations of dynamic thermoviscoelasticity, the heat equation with the Joule heating term, and the quasistatic charge conservation equation. The system is strongly nonlinear since the electrical conductivity...

article

Sampled-data control and stability of sets for nonlinear systems

Éva Gyurkovics

Differential Equations and Dynamical Systems > 2009 > 17 > 1-2 > 169-183

This paper is devoted to the investigation of the relation between stability properties of nonlinear closed-loop control systems and those of families of approximations with respect to a given set. Firstly, such relation is derived for continuous-time closed-loop systems and the associated sampled-data systems. Secondly, stability results are presented for parametrized families of exact and approximate...

article

Editorial

Differential Equations and Dynamical Systems > 2009 > 17 > 1-2 > 1-2

INFONA - science communication portal

Differential Equations and Dynamical Systems

Almost periodic solutions of a functional differential equation by monotone iterative method

Hopf bifurcation and periodic solutions in a dynamical model for HIV and immune response

Dynamics in numerics: On a discrete predator-prey model

Existence and multiplicity of positive and negative solutions for higher-order multi-point Sturm-Liouville boundary value problems

Multiple positive solutions for nonlinear third order general three-point boundary value problems

Editorial

Korteweg-de Vries-Burgers equation with a higher-order nonlinearity

Dynamical models for the development of unilingual society into bilingual society

Bifurcation analysis in an age-structured model of single species living in two identical patches

Stochastic dynamics and passage times for diffusion approximations

Oscillation of mixed neutral functional differential equations with distributed deviating arguments

Mathematical analysis of the role of repeated exposure on malaria transmission dynamics

Effect of small time delay in a predator-prey model within random environment

Almost periodic solutions of nonlinear functional differential equations

Stability of the second order delay differential equations with a damping term

On bifurcation and chaos in a discrete dynamical system

A Kolmogorov-Fokker-Planck approach for a stochastic Duffing-van der Pol system

Existence for the thermoviscoelastic thermistor problem

Sampled-data control and stability of sets for nonlinear systems

Editorial

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