Kato Chaos in Linear Dynamics

Non-linear dynamics, chaos and phase transitions in DNA molecule

DNA molecule is a complex dynamical system consisting of many atoms having a quasi-one-dimensional structure. In this paper, we first review non-linear Hamiltonian DNA dynamics in the form of several Peyrard-Bishoptype DNA models. Then, we explore Hamiltonian chaos and thermodynamical phase transitions related to Hamiltonian DNA dynamics. These second-order phase transitions are shown to have t...

CONTROL OF CHAOS IN A DRIVEN NON LINEAR DYNAMICAL SYSTEM

We present a numerical study of a one-dimensional version of the Burridge-Knopoff model [16] of N-site chain of spring-blocks with stick-slip dynamics. Our numerical analysis and computer simulations lead to a set of different results corresponding to different boundary conditions. It is shown that we can convert a chaotic behaviour system to a highly ordered and periodic behaviour by making on...

Rich dynamics in multi-strain models: non-linear dynamics and deterministic chaos in dengue fever epidemiology

Existence theorems in linear chaos

Chaotic linear dynamics deals primarily with various topological ergodic properties of semigroups of continuous linear operators acting on a topological vector space. We treat the questions of the following type. Characterize which of the spaces from a given class support a semigroup of prescribed shape satisfying a given topological ergodic property. In particular, we characterize LBS-spaces (...

Chaos without nonlinear dynamics.

A linear, second-order filter driven by randomly polarized pulses is shown to generate a waveform that is chaotic under time reversal. That is, the filter output exhibits determinism and a positive Lyapunov exponent when viewed backward in time. The filter is demonstrated experimentally using a passive electronic circuit, and the resulting waveform exhibits a Lorenz-like butterfly structure. Th...