Analytical Studies on Diffusion and lntermittency in Chaotic Maps

The study of simple chaotic maps for non-equilibrium processes in statistical physics has been one of the central themes in the theory of chaotic dynamical systems. Recently, many works have been carried out on deterministic diffusion in spatially extended one-dimensional maps This can be related to real physical systems such as Josephson junctions in the presence of microwave radiation and parametrically driven oscillators. Transport due to chaos is an important problem in Hamiltonian dynamics also. A recent approach is to evaluate the exact diffusion coefficient in terms of the periodic orbits of the system in the form of cycle expansions. But the fact is that the chaotic motion in such spatially extended maps has two complementary aspects- - diffusion and interrnittency. These are related to the time evolution of the probability density function which is approximately Gaussian by central limit theorem. It is noticed that the characteristic function method introduced by Fujisaka and his co-workers is a very powerful tool for analysing both these aspects of chaotic motion. The theory based on characteristic function actually provides a thermodynamic formalism for chaotic systems It can be applied to other types of chaos-induced diffusion also, such as the one arising in statistics of trajectory separation. It was noted that there is a close connection between cycle expansion technique and characteristic function method. It was found that this connection can be exploited to enhance the applicability of the cycle expansion technique. In this way, we found that cycle expansion can be used to analyse the probability density function in chaotic maps. In our research studies we have successfully applied the characteristic function method and cycle expansion technique for analysing some chaotic maps. We introduced in this connection, two classes of chaotic maps with variable shape by generalizing two types of maps well known in literature.

Decreased GyBAA Receptor Function in the Brain Stem during Pancreatic Regeneration in Rats

Gamma amino outyric acid is a major inhibitory neurotrarsr titter in the central nervous system. In the preset study sv, Have investigate(' the alteration of GABA receptor, In t he hrain stem of rats during pancreatic regeneration. Three groups of rats were used for the study: sham operated, 72 It and 7 days partially pancreatectonnsea. GABA was (juan- (ified by [H]GABA receptor iispiacement method. GABA receptor kin: 10, pat at i et•ers were studied by using the binding of F'.](iAhA as ligand to the Triton X-100 treated me,i1,;-:mes a1,J displacement with unlabelled GABA. GhRA,v receptor activity was studied by using the [` -1 h3cuculline and displacement with unlabellecV euculline. ;.\13A content significantly decreased (1' < (1.(101 ) it, 0-e brain stern during the regeneration of pancreas. 'I hl, high affinity (IAI3A receptor binding sho?:ed it sigii'f cant decrease in 131„.,\ (P < 11.01) and K,I 1).05) n 72 h and 7 days after partial pancreatee 'timv. ";:flhicuculline hin(Iing showed it signih eat, 'le ( r(, :,e in /Jn1,s and K,I (P < 0.001) in 72 h pa^.rcreaw,, mised rats when compared with sham wt--tt' as P,n and K,I reversed to near sham after 7 da,s of pancreatectomv. The results sugge,) that GAB A throur,r; ('GABA receptors in brain Atcem has a regulatory uie during active regeneration of pancreas which will have inunense clinical significance in the treatment of cliahetcs.

Studies on function projective synchronization in chaotic and hyperchaotic systems

FPS is a more general form of synchronization. Hyperchaotic systems possessing more than one positive Lypaunov exponent exhibit highly complex behaviour and are more suitable for some applications like secure communications. In this thesis we report studies of FPS and MFPS of a few chaotic and hyperchaotic systems. When all the parameters of the system are known we show that active nonlinear control method can be efectively used to obtain FPS. Adaptive nonlinear control and OPCL control method are employed for obtaining FPS and MFPS when some or all parameters of the system are uncertain. A secure communication scheme based on MFPS is also proposed in theory. All our theoretical calculations are verified by numerical simulations.

Message Integrity in the World Wide Web: Use of Nested Hash Function and a Fast Stream Cipher

The focus of this work is to provide authentication and confidentiality of messages in a swift and cost effective manner to suit the fast growing Internet applications. A nested hash function with lower computational and storage demands is designed with a view to providing authentication as also to encrypt the message as well as the hash code using a fast stream cipher MAJE4 with a variable key size of 128-bit or 256-bit for achieving confidentiality. Both nested Hash function and MAJE4 stream cipher algorithm use primitive computational operators commonly found in microprocessors; this makes the method simple and fast to implement both in hardware and software. Since the memory requirement is less, it can be used for handheld devices for security purposes.