Thanjavur, India
Thanjavur, India

The Tamil University, Thanjavur, in Tamil Nadu, India, was established to provide higher research in the Tamil language and advanced study in allied branches such as linguistics, translation, lexicography, music, drama and manuscriptology. M.Phil and Ph.D programmes were introduced in 1992 for disciplines such as Language, Literature, Translation, and Sculpture.The university has six science departments namely Industries and Earth science, Computer Science, Environmental and Herbal Science, Siddha Medicine, Ancient science and Architecture.The Ocean and Atmospheric science and Technology Cell, an autonomous body supported by the Ministry of Earth science, New Delhi is under the Department of Industries and Earth science. Wikipedia.

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Vaidyanathan S.,Tamil University
International Journal of PharmTech Research | Year: 2015

Chaos theory has important applications in Science and Engineering. Recently, there is an active research on the applications of chaos theory to many real-world systems including the biological systems. Nerve membranes are known to exhibit their own nonlinear dynamics which generate and propagate action potentials. Such nonlinear dynamics in nerve membranes can produce chaos in neurons and related bifurcations. In 1952, A.L. Hodgkin and A.F. Huxley proposed a nonlinear dynamical system as a mathematical model of nerve membranes based on their electrophysiological experiments with squid giant atoms. Chaos in nerve membranes have been studied in the chaos literature both theoretically and experimentally. In this research work, we discuss the properties of the Birkhoff-Shaw strange chaotic attractor (1981), which is a forced oscillator. Birkhoff-Shaw strange chaotic attractor exhibits the structure of beaks and wings, typically observed in chaotic neuronal models. We also derive new results for the synchronization of identical Birkhoff-Shaw chaotic attractors via adaptive control method. All the main results for the Birkhoff-Shaw chaotic attractor are proved using Lyapunov stability theory. Also, numerical simulations have been plotted using MATLAB to illustrate the main results for the Birkhoff-Shaw chaotic attractor. © 2015, Sphinx Knowledge House. All right reserved.


Vaidyanathan S.,Tamil University
International Journal of PharmTech Research | Year: 2015

Chaos is an important applied area in nonlinear dynamical systems and it is applicable to many real-world systems including the biological systems. Nerve membranes are known to exhibit their own nonlinear dynamics which generate and propagate action potentials. Such nonlinear dynamics in nerve membranes can produce chaos in neurons and related bifurcations. In 1952, A.L. Hodgkin and A.F. Huxley proposed a nonlinear dynamical system as a mathematical model of nerve membranes based on their electrophysiological experiments with squid giant atoms. Chaos in nerve membranes have been studied in the chaos literature both theoretically and experimentally. In this research work, we discuss the properties of the Birkhoff-Shaw chaotic attractor, which is a forced oscillator and this strange chaotic attractor exhibits the structure of beaks and wings, typically observed in chaotic neuronal models. We also derive new results for the adaptive control of the Birkhoff-Shaw chaotic attractor (1981).All the main results are proved using Lyapunov stability theory. Also, numerical simulations have been plotted using MATLAB to illustrate the main results for the Birkhoff-Shaw chaotic attractor. © 2015, Sphinx Knowledge House. All right reserved.


Vaidyanathan S.,Tamil University
International Journal of PharmTech Research | Year: 2015

Since the recent research has shown the importance of biological control in many biological systems appearing in nature, this research paper investigates research in the dynamic and chaotic analysis of the generalized Lotka-Volterra three-species biological system, which was studied by Samardzija and Greller (1988). The generalized Lotka-Voterra biological system consists of two predator and one prey populations. This paper depicts the phase portraits of the 3-D generalized Lotka-Volttera system when the system undergoes chaotic behaviour. The synchronization of master and slave chaotic systems deals with synchronizing the respective states of the two systems asymptotically with time. Next, this paper derives adaptive biological control law for globally and exponentially synchronizing the states of the generalized Lotka-Volterra three-species biological systems with unknown parameters. All the main results are proved using Lyapunov stability theory. Also, numerical simulations have been plotted using MATLAB to illustrate the main results for the three-species generalized Lotka-Volterra biological system and its adaptive synchronization. © 2015, Sphinx Knowledge House. All right reserved.


Vaidyanathan S.,Tamil University
International Journal of PharmTech Research | Year: 2015

Recent research has shown the importance of biological control in many biological systems appearing in nature. This paper investigates research in the dynamic and chaotic analysis of the generalized Lotka-Volterra three-species biological system, which was studied by Samardzija and Greller (1988). The generalized Lotka-Voterra biological system consists of two predator and one prey populations. This paper displays the phase portraits of the 3-D generalized Lotka-Volttera system when the system undergoes chaotic behaviour. Next, this paper derives adaptive biological control for globally stabilizing the trajectories of the generalized Lotka-Volterra three-species biological system with unknown parameters. All the main results are proved using Lyapunov stability theory. Also, numerical simulations have been plotted using MATLAB to illustrate the main results for the three-species generalized Lotka-Volterra biological system. © 2015, Sphinx Knowledge House. All rights reserved.


Vaidyanathan S.,Tamil University
International Journal of PharmTech Research | Year: 2015

In this research work, we first discuss the properties of the 3-cells CNN attractor discovered by Arena et al. (1998). Recent research has shown the importance of biological control in many biological systems appearing in nature. In computer science, machine learning and biology, cellular neural networks (CNN) are a parallel computing paradigm, similar to neural networks with the difference that communication is allowed between neighbouring units only. CNN has wide applications and recently, CNN is found to have many applications in biology and applied areas of biology. Chua and Yang introduced the cellular neural network (CNN) in 1988 as a nonlinear dynamical system composed by an array of elementary and locally interacting nonlinear subsystems, which are called cells. We also derive new results for the adaptive biological synchronization of the identical 3-cells CNN attractors. All the main results are proved using Lyapunov stability theory. Also, numerical simulations have been plotted using MATLAB to illustrate the main results for the 3-cells cellular neural network (CNN) attractor. © 2015, Sphinx Knowledge House. All right reserved.


Vaidyanathan S.,Tamil University
International Journal of PharmTech Research | Year: 2015

Chaos in nonlinear dynamics occurs widely in physics, chemistry, biology, ecology, secure communications, cryptosystems and many other scientific disciplines. Chaotic systems have many important applications in science and engineering. This paper derives new results for the analysis and adaptive control of a chemical chaotic attractor discovered by Haung (2005). This paper starts with a detailed description of the chemical reactor dynamics and the parameter values for which the chemical reactor exhibits chaotic behaviour. Next, adaptive control law is devised for the global chaos control of the chemical chaotic reactor with unknown parameters. The main results for adaptive control of the chemical chaotic attractor are established using Lyapunov stability theory. Next, the main results are illustrated with numerical simulations using MATLAB. © 2015, Sphinx Knowledge House. All rights reserved.


Vaidyanathan S.,Tamil University
International Journal of PharmTech Research | Year: 2015

In the recent decades, there is significant interest in the literature in the application of chaos in physical, electrical, chemical and biological systems. This paper investigates research in the dynamic analysis and global chaos synchronization of enzymessubstrate reactions system with ferroelectric behaviour in brain waves which was studied by Enjieu Kadji, Chabi Orou, Yamapi and Woafo (2007). The enzymes-substrates system is a 2-D non-autonomous system with a cosinusoidal forcing term. This paper depicts the phase portraits of the 2-D enzymes-substrates system when the system undergoes chaotic behaviour. Next, this paper derives new adaptive control results for globally synchronizing the identical enzymesubstrates systems with uncertain parameters. Backstepping control is used to derive the main results for global synchronization of the enzyme-substrates systems. MATLAB plots have been shown in this paper to illustrate the main results for the enzyme-substrates system. © 2015, Sphinx Knowledge House. All right reserved.


Vaidyanathan S.,Tamil University
International Journal of PharmTech Research | Year: 2015

Recent research has shown the importance of biological control in many biological systems appearing in nature. In computer science, machine learning and biology, cellular neural networks (CNN) are a parallel computing paradigm, similar to neural networks with the difference that communication is allowed between neighbouring units only. CNN has wide applications and recently, CNN is found to have many applications in biology and applied areas of biology. Chua and Yang introduced the cellular neural network (CNN) in 1988 as a nonlinear dynamical system composed by an array of elementary and locally interacting nonlinear subsystems, which are called cells. In this research work, we discuss the properties of the 3-cells CNN attractor discovered by Arena et al. (1998). We also derive new results for the adaptive biological control of the 3-cells CNN attractor. All the main results are proved using Lyapunov stability theory. Also, numerical simulations have been plotted using MATLAB to illustrate the main results for the 3-cells cellular neural network (CNN) attractor. © 2015, Sphinx Knowledge House. All rights reserved.


Vaidyanathan S.,Tamil University
International Journal of PharmTech Research | Year: 2015

Chaos theory has a lot of applications in science and engineering. This paper first details the qualitative properties of the forced Van der Pol chaotic oscillator, which has important applications. Since its introduction in the 1920’s, the Van der Pol equation has been a prototype model for systems with self-excited limit cycle oscillations. The Van der Pol equation has been studied over wide parameter regimes, from perturbations of harmonic motion to relaxation oscillations. It has been used by scientists to model a variety of physical and biological phenomena. Next, we derive new results for the global chaos synchronization of the identical forced Van der Pol chaotic oscillators via adaptive control method. MATLAB plots have been shown to illustrate the phase portraits of the forced Van der Pol chaotic oscillator and the adaptive synchronization of the forced Van der Pol chaotic oscillator. © 2015, Sphinx Knowledge House. All right reserved.


Vaidyanathan S.,Tamil University
International Journal of PharmTech Research | Year: 2015

Lotka-Volterra population biology models are important models that describe the interaction between various biological species considered as predator-prey system. This work describes a Lotka-Volterra population biology model with negative feedback. We show that for this biological model, the predator and prey species have stable coexistence. Then we shall propose ecological monitoring of the population biology model by constructing a nonlinear exponential observer for the population biology model under study. The nonlinear observer design for the population biology model is constructed by applying Sundarapandian’s theorem (2002) and using only the dynamicsof the Lotka-Volterra population biology model and the prey population size as the output function. Numerical example and MATLAB simulations are given to illustrate the ecological monitoring or the nonlinear observer design for the two-species Lotka- Volterra population biology model with negative feedback. © 2015, Sphinx Knowledge House. All right reserved.

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