The type of symmetry exhibited by a travelling wave can have important implications for its behaviour and properties, such as polarization, dispersion, interactions with other waves or boundaries. fractional differential Duffing problem refers to the mathematical modelling nonlinear, damped oscillations system derivatives. It is generalization classical equation, which describes oscillator (the...

Nonlinear oscillators with hardening and softening cubic Duffing nonlinearity are considered. Such classical conservative oscillators are known to have an amplitude-dependent period. In this work, we design oscillators with the Duffing-type restoring force but an amplitude-independent period. We present their Lagrangians, equations of motion, conservation laws, as well as solutions for motion.

We use Elie Cartan's method of equivalence to give a complete classification, in terms of differential invariants, of second-order ordinary differential equations admitting Lie groups of fibre-preserving point symmetries. We then apply our results to the determination of all second-order equations which are equivalent, under fibre-preserving transformations, to the free particle equation. In ad...

Information signal embedded in a chaotic transmitter can be recovered by a receiver if it is a replica of the transmitter. In this paper, a new aspect of chaotic communication is introduced. A sliding-mode observer replaces the conventional chaotic system at the receiver side, which does not need information from the transmitter. So the uncertainties in the transmitter and the transmission line...

A stochastic Duffing-type oscillator model, i.e noise-driven motion with inertia in a potential landscape, is considered for glacial millennial-scale climate transitions. The potential and noise parameters are estimated from a Greenland ice-core record using a nonlinear Kalman filter. For the period from 60 to 20 ky before present, a bistable potential with a deep well corresponding to a cold s...

We prove that when subjected to periodic forcing of the form pμ,ρ,ω(t) = μ(ρh(x, y) + sin(ωt)), certain 2-dimensional vector fields with dissipative homoclinic loops admit strange attractors with SRB measures for a set of forcing parameters (μ, ρ, ω) of positive Lebesgue measure. The proof extends ideas of Afraimovich and Shilnikov [1] and applies the recent theory of rank 1 maps developed by W...