In recent years, there has been an expanding research on the applications of fractional calculus to the areas of signal processing, modeling, and controls. Analog circuit implementation of chaotic systems is used in studying the nonlinear dynamical phenomena, as well as applied in realizing the controller development. In this paper, chain fractance and tree fractance circuits are constructed to...

The influence of periodic perturbations to a Lotka–Volterra system, modeling a competition between three species, is studied, provided that in the unperturbed case the system has a unique attractor — a contour of heteroclinic orbits joining unstable equilibria. It is shown that the perturbed system may manifest regular behavior corresponding to the existence of a smooth invariant torus, and, as...

We discuss the time-discrete parametrized dynamics of two neuromodules, which are coupled in a uni-directional way. General conditions for the existence of synchronized dynamics are derived for these systems. It is demonstrated that already the one-way couplings of 2-neuron modules can result in periodic, quasiperiodic as well as chaotic dynamics constrained to a synchronization manifold M . St...

We measure Anderson localization in quasi-one-dimensional waveguides in the presence of absorption by analyzing the echo dynamics due to small perturbations. We specifically show that the inverse participation number of localized modes dictates the decay of the Loschmidt echo, differing from the Gaussian decay expected for diffusive or chaotic systems. Our theory, based on a random matrix model...

We show that finite Fermi systems governed by a mean field and a few-body interaction generically possess spectral fluctuations of the Wigner-Dyson type and are, thus, chaotic. Our argument is based on an analogy to the metal-insulator transition. We construct a sparse random-matrix scaffolding ensemble (ScE) that mimics this transition. Our claim then follows from the fact that the generic ran...

This paper deals with the problem of nonlinear time series prediction. The method uses a couple of lters to decompose iteratively the series. This sc heme leads to a time series whic h con tains the slo w est dynamics and a hierarchy of detail time series which contain intermediate, up to the highest, dynamics. The new series are then used for modeling and predicting. The result obtained on the...

Nurses often practice in chaotic, demanding work environments. Understanding the negative impact these environments have on nurses and patients is paramount to halting this epidemic. Researchers' decade-old call for administrators and managers to correct this occupational hazard is ineffective in decreasing the effects of prolonged work-related stress on nurses. Staff development educators' mod...

Modeling of human and animal behavior is of interest for a number of diagnostic purposes. Convolutional neural networks offer a constructive approach allowing learning on a limited number of examples. Chaotic tendencies make that learning is not always successful. The paper looks into a number of applications to find the reason for this anomaly and identifies the need for behavioral references ...

We present a formulation of a fuzzy logic system (FLS) that can be used to construct nonparametric models of nonlinear processes, given only input–output data. In order to effectively construct such models, we discuss several design methods with different properties and features. We compare and illustrate systems designed with each one of the methods, using an example on the predictive modeling...

The existence of a Hamiltonian vector field in which trajectories of the invariant set of a dissipative hyperbolic chaotic system are embedded will be proved (see notation below). Evidence of this with an example concerning the Lorenz system will be provided. Also, a constructive method of designing a Hamiltonian for the Lorenz attractor with a universal approximator will be introduced. The pre...