• Sujit K Bose

Articles written in Proceedings – Mathematical Sciences

• Transformation of chaotic nonlinear polynomial difference systems through Newton iterations

Chaotic sequences generated by nonlinear difference systems or ‘maps’ where the defining nonlinearities are polynomials, have been examined from the point of view of the sequential points seeking zeroes of an unknown functionf following the rule of Newton iterations. Following such nonlinear transformation rule, alternative sequences have been constructed showing monotonie convergence. Evidently, these are maps of the original sequences. For second degree systems, another kind of possibly less chaotic sequences have been constructed by essentially the same method. Finally, it is shown that the original chaotic system can be decomposed into a fast monotonically convergent part and a principal oscillatory part showing sharp oscillations. The methods are exemplified by the well-known logistic map, delayed-logistic map and the Hénon map.

• Boundary stabilization of a hybrid Euler—Bernoulli beam

We consider a problem of boundary stabilization of small flexural vibrations of a flexible structure modeled by an Euler-Bernoulli beam which is held by a rigid hub at one end and totally free at the other. The hub dynamics leads to a hybrid system of equations. By incorporating a condition of small rate of change of the deflection with respect tox as well ast, over the length of the beam, for appropriate initial conditions, uniform exponential decay of energy is established when a viscous boundary damping is present at the hub end.

• On initial conditions for a boundary stabilized hybrid Euler-Bernoulli beam

We consider here small flexural vibrations of an Euler-Bernoulli beam with a lumped mass at one end subject to viscous damping force while the other end is free and the system is set to motion with initial displacementy0(x) and initial velocityy1 (x). By investigating the evolution of the motion by Laplace transform, it is proved (in dimensionless units of length and time) that$$\smallint _0^1 y_{xt}^2 dx \leqslant \smallint _0^1 y_{xx}^2 dx,t &gt; t_0$$, wheret0 may be sufficiently large, provided that {y0,y1} satisfy very general restrictions stated in the concluding theorem. This supplies the restrictions for uniform exponential energy decay for stabilization of the beam considered in a recent paper.

• Uniform stability of damped nonlinear vibrations of an elastic string

Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess energy uniformly bounded by exponentially decaying function of time. The result is achieved by considering an energy-like Lyapunov functional for the system.

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019