Balachandran Krishnan | Bharathiar University, Coimbatore, Tamilnadu, INDIA (original) (raw)

Balachandran Krishnan

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Papers by Balachandran Krishnan

Research paper thumbnail of Existence of solutions for quasilinear delay integrodifferential equations with nonlocal conditions

Electronic Journal of Differential Equations, 2009

We prove the existence and uniqueness of mild and classical solution to a quasilinear delay integ... more We prove the existence and uniqueness of mild and classical solution to a quasilinear delay integrodifferential equation with nonlocal condition. The results are obtained by using C 0 -semigroup and the Banach fixed point theorem.

Research paper thumbnail of Spatiotemporal dynamics of a predator-prey model incorporating a prey refuge

Journal of Applied Analysis and Computation, Mar 12, 2013

In this paper, we investigate the spatiotemporal dynamics of a ratio-dependent predator-prey mode... more In this paper, we investigate the spatiotemporal dynamics of a ratio-dependent predator-prey model with cross diffusion incorporating proportion of prey refuge. First we get the critical lines of Hopf and Turing bifurcations in a spatial domain by using mathematical theory. More specifically, the exact Turing region is given in a two parameter space. Also we perform a series of numerical simulations. The obtained results reveal that this system has rich dynamics, such as spotted, stripe and labyrinth patterns which show that it is useful to use the predator-prey model to reveal the spatial dynamics in the real world.

Research paper thumbnail of Approximate controllability of neutral stochastic integrodifferential systems in Hilbert spaces

Electronic Journal of Differential Equations, 2008

In this paper sufficient conditions are established for the controllability of a class of neutral... more In this paper sufficient conditions are established for the controllability of a class of neutral stochastic integrodifferential equations with nonlocal conditions in abstract space. The Nussbaum fixed point theorem is used to obtain the controllability results, which extends the linear system to the stochastic settings with the help of compact semigroup. An example is provided to illustrate the theory.

Research paper thumbnail of Existence of mild solutions for quasilinear integrodifferential equations with impulsive conditions

Page 1. Electronic Journal of Differential Equations, Vol. 2009(2009), No. 84, pp. 1–9. ISSN: 107... more Page 1. Electronic Journal of Differential Equations, Vol. 2009(2009), No. 84, pp. 1–9. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu EXISTENCE OF MILD SOLUTIONS ...

Research paper thumbnail of Controllability of Stochastic Impulsive Neutral Integrodifferential Systems with Infinite Delay

Journal of Nonlinear Analysis and Optimization Theory Applications, Dec 20, 2012

Research paper thumbnail of Controllability of fractional dynamical systems with prescribed controls

IET Control Theory & Applications, 2013

ABSTRACT The present study deals with the controllability results for fractional dynamical system... more ABSTRACT The present study deals with the controllability results for fractional dynamical systems with prescribed controls. Sufficient conditions for the controllability results of non-linear fractional dynamical systems are obtained using Schauder's fixed point theorem and fractional calculus. Illustrative examples are presented.

Research paper thumbnail of CONTROLLABILITY OF NONLINEAR STOCHASTIC SYSTEMS WITH MULTIPLE TIME–VARYING DELAYS IN CONTROL

This paper is concerned with the problem of controllability of semi-linear stochastic systems wit... more This paper is concerned with the problem of controllability of semi-linear stochastic systems with time varying multiple delays in control in finite dimensional spaces. Sufficient conditions are established for the relative controllability of semi-linear stochastic systems by using the Banach fixed point theorem. A numerical example is given to illustrate the application of the theoretical results. Some important comments are also presented on existing results for the stochastic controllability of fractional dynamical systems.

Research paper thumbnail of Existence of solutions for quasilinear delay integrodifferential equations with nonlocal conditions

Electronic Journal of Differential Equations, 2009

We prove the existence and uniqueness of mild and classical solution to a quasilinear delay integ... more We prove the existence and uniqueness of mild and classical solution to a quasilinear delay integrodifferential equation with nonlocal condition. The results are obtained by using C 0 -semigroup and the Banach fixed point theorem.

Research paper thumbnail of Spatiotemporal dynamics of a predator-prey model incorporating a prey refuge

Journal of Applied Analysis and Computation, Mar 12, 2013

In this paper, we investigate the spatiotemporal dynamics of a ratio-dependent predator-prey mode... more In this paper, we investigate the spatiotemporal dynamics of a ratio-dependent predator-prey model with cross diffusion incorporating proportion of prey refuge. First we get the critical lines of Hopf and Turing bifurcations in a spatial domain by using mathematical theory. More specifically, the exact Turing region is given in a two parameter space. Also we perform a series of numerical simulations. The obtained results reveal that this system has rich dynamics, such as spotted, stripe and labyrinth patterns which show that it is useful to use the predator-prey model to reveal the spatial dynamics in the real world.

Research paper thumbnail of Approximate controllability of neutral stochastic integrodifferential systems in Hilbert spaces

Electronic Journal of Differential Equations, 2008

In this paper sufficient conditions are established for the controllability of a class of neutral... more In this paper sufficient conditions are established for the controllability of a class of neutral stochastic integrodifferential equations with nonlocal conditions in abstract space. The Nussbaum fixed point theorem is used to obtain the controllability results, which extends the linear system to the stochastic settings with the help of compact semigroup. An example is provided to illustrate the theory.

Research paper thumbnail of Existence of mild solutions for quasilinear integrodifferential equations with impulsive conditions

Page 1. Electronic Journal of Differential Equations, Vol. 2009(2009), No. 84, pp. 1–9. ISSN: 107... more Page 1. Electronic Journal of Differential Equations, Vol. 2009(2009), No. 84, pp. 1–9. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu EXISTENCE OF MILD SOLUTIONS ...

Research paper thumbnail of Controllability of Stochastic Impulsive Neutral Integrodifferential Systems with Infinite Delay

Journal of Nonlinear Analysis and Optimization Theory Applications, Dec 20, 2012

Research paper thumbnail of Controllability of fractional dynamical systems with prescribed controls

IET Control Theory & Applications, 2013

ABSTRACT The present study deals with the controllability results for fractional dynamical system... more ABSTRACT The present study deals with the controllability results for fractional dynamical systems with prescribed controls. Sufficient conditions for the controllability results of non-linear fractional dynamical systems are obtained using Schauder's fixed point theorem and fractional calculus. Illustrative examples are presented.

Research paper thumbnail of CONTROLLABILITY OF NONLINEAR STOCHASTIC SYSTEMS WITH MULTIPLE TIME–VARYING DELAYS IN CONTROL

This paper is concerned with the problem of controllability of semi-linear stochastic systems wit... more This paper is concerned with the problem of controllability of semi-linear stochastic systems with time varying multiple delays in control in finite dimensional spaces. Sufficient conditions are established for the relative controllability of semi-linear stochastic systems by using the Banach fixed point theorem. A numerical example is given to illustrate the application of the theoretical results. Some important comments are also presented on existing results for the stochastic controllability of fractional dynamical systems.

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