Asesh Roy Chowdhury

Synchronization between variable time-delayed systems and cryptography

In this letter we consider the phenomena of chaos synchronization for time-delayed dynamical systems when the delay is not constant. As an example we have considered the autonomous continuous-time-delayed system studied by Ucar, when the delay is modulated. The region in the parameter space for the onset of chaos is explored and both analytical and numerical methodologies are used for the analysis of the synchronization of two such systems, using the Krasovskii-Lyapunov functional. We have applied the adaptive coupling method for synchronization and studied the implementation of cryptography for this coupled system. The message extraction procedure is illustrated with the help of simulated results.

Quantum integrable systems

NONLINEAR SYSTEMS AND CLASSICAL IST Introduction Definition of Integrability Lax Pair Technique Inverse Scattering Transform Hamiltonian Structure COORDINATE BETHE ANSATZ Introduction Nonlinear Systems and the CBA Fermionic System Boundary Condition in Bethe Ansatz Heisenberg Spin Chain Spin of the Bethe Ansatz State Other Integrable Models YANG-BAXTER EQUATION Introduction General Description Factorized Scattering Baxters Star Triangle Relation Vertex Models Reflection Equation Algebra CONTINUOUS INTEGRABLE SYSTEMS Introduction Quantum Continuous Integrable Systems Conserved Quantities Nonultralocal systems and the YBE Operator Product Expansion and YBE Finite Boundary Conditions Modified Classical Yang-Baxter Equation ALGEBRAIC BETHE ANSATZ Introduction Discrete Self Trapping Model Asymmetric XXZ Model in a Magnetic Field Analytical Bethe Ansatz Off-Shell Bethe Ansatz Nested Bethe Ansatz Fusion Procedure Fusion Procedure for Open chains Fusion Procedure for Transfer Matrices Application of Fusion Procedure INTEGRABLE LONG-RANGE MODELS Introduction Long-Range Models from the ABA Symmetry Transformation Calogero-Moser Models SEPARATION OF VARIABLES Introduction Hamilton-Jacobi Equation Sklyanins Method for SoV Goryachev-Chaplygin Top Quantum Case and the Role of Lie Algebra Bi-Hamiltonian Structure and SoV SoV for GCM Model SoV and Boundary Conditions BACKLUND TRANSFORMATIONS Introduction Permutability Theorem Backlund Transformations and Classical Inverse Scattering Backlund Transformations from Riccati Equation Darboux Backlund Transformations The Exponential Lattice Canonical Transformations Group Property of Backlund Transformations Recent Developments in Backlund Transformation Theory Sklyanins Formalism for Canonical Backlund Transformations Extended Phase Space Method Quantization of Backlund Transformations Method of Projection Operators QUANTUM GLM EQUATION Introduction Quantum GLM Equation Quantum Floquet Function Exact Quantization Quantum GLM Equation in a Continuous System Bound States and an Alternative Approach APPENDICES Direct Product Calculus Grassman Algebra Bethe Ansatz Equation AKNS Problem BIBLIOGRAPHY INDEX

On Some Properties of Cylindrically Transformed Systems With R(π) Symmetry and Phase Dynamics

Nonlinear dynamical systems with R( ) symmetry are shown to behave in a very interesting manner under a new transformation of dynamical variables. Such property helps to identify the phase dynamics embedded in the system but preserves the basic property of the attractor intact. This is very similar to those phenomenon discussed with the help of covering transformation in the literature. The Poincare sections obtained are identical to those obtained through covering transformation and hence indicate to a similar topological structure and identical dynamical characteristics.

A New Asymmetric Long-Range Model and Algebraic Bethe Ansatz

A new integrable long-range model is derived from a new asymmetric R-matrix recently discussed by Bibikov in relation to a XXZ spin chain in an external magnetic field. The algebraic Bethe Ansatz is used to derive the eigenvalues and equations for the eigen momenta both for the usual and long-range model.