Bifurcations and the structure of limit sets are studied for a three-dimensional Chua’s circuit system with a cubic nonlinearity. On the base of both computer simulations and theoretical results a model map is proposed which allows one to follow the evolution in the phase space from a simple (Morse-Smale) structure to chaos. It is established that the appearance of a complex, multistructural se...

This paper explores the combination of self-organizing map (SOM) and feedback, in order to represent sequences of inputs. In general, neural networks with time-delayed feedback represent time implicitly, by combining current inputs and past activities. It has been difficult to apply this approach to SOM, because feedback generates instability during learning. We demonstrate a solution to this p...

We revisit the globally coupled map lattice. We show that in the so called turbulent regime various periodic cluster attractor states are formed, even though the coupling between the maps are very small relative to the nonlinearity in the element maps. Most outstanding is a maximally symmetric three cluster attractor in period-3 motion, due to the foliation of the period-3 window of the element...

We evaluate the leading asymptotic contributions to the traces of the quantum baker’s map propagator. Besides the usual Gutzwiller periodic orbit contribution, we identify boundary paths giving rise to anomalous log h̄ terms. Some examples of these anomalous terms are calculated both numerically and analytically. Submitted to Nonlinearity Permanent address: Centro Brasileiro de Pesquisas F́ısicas...

Multi-peaked localized stationary solutions of the discrete nonlinear Schrödinger (DNLS) equation are presented in one (1D) and two (2D) dimensions. These are excited states of the discrete spectrum and correspond to multi-breather solutions. A simple, very fast, and efficient numerical method, suggested by Aubry, has been used for their calculation. The method involves no diagonalization, but ...

We consider the ultrasound imaging problem governed by a nonlinear wave equation of Westervelt type with variable speed. show that coefficient nonlinearity can be recovered uniquely from knowledge Dirichlet-to-Neumann map. Our proof is based on second order linearization and use Gaussian beam solutions to reduce inversion weighted geodesic ray transform. propose an algorithm report results nume...

typically, two configurations are used for energy harvesting, with different advantages: piezoelastic and piezomagnetoelastic. best performance of piezoelastic configuration is limited to its narrow bandwidth around the resonance frequency. if the excitation frequency slightly deviates from the resonance frequency, the power-out is severely reduced. to overcome this, the piezomagnetoelastic has...

In this work we characterize the escape of orbits from phase space Riemann–Liouville (RL) fractional standard map (fSM). The RL-fSM, given in action–angle variables, is derived equation motion kicked rotor when second order derivative substituted by a RL α. Thus, RL-fSM parameterized K and α∈(1,2] which control strength nonlinearity derivative, respectively. Indeed, for α=2 initial conditions, ...

Testing of ADC differential nonlinearity by the histogram method requires a signal generator with extremely low distortion and high stability. In this paper, the new type of stimulus signal is proposed, which simplifies the task. The testing signal has an exponential form and can be generated simply by discharging the capacitor across the resistance. The resulting digital samples from the outpu...

We investigate the Cauchy problem for a nonlocal (two-place) FORQ equation. By interpreting this equation as special case of two-component peakon system (exhibiting cubic nonlinearity), we convert into ordinary differential equations in Banach space. Using approach, are able to demonstrate local well-posedness Sobolev space Hs where s>5/2. also establish continuity properties data-to-solution m...