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Two elastically coupled nanomechanical resonators driven independently near their resonance frequencies show intricate nonlinear dynamics. The dynamics provide a scheme for realizing a nanomechanical system with tunable frequency and…
Rotobreathers in the chain of coupled linearly elastic rotators are analyzed. Each rotator is a particle connected by a massless elastic rod with a frictionless pivot; it has two degrees of freedom, length and angle of rotation. The rods of…
A novel process is described that produces horizontal size segregation in a vertically vibrated layer of granular material. The behavior is a consequence of two distinct phenomena that are unique to excited granular media: vibration which…
For nuclei with N = Z, the isospin degree of freedom is important and, for deformed systems, rotational bands of different isospin may be expected at low excitation energies. We have investigated, in a simple model space, the influence of…
A piecewise-linear model with a single degree of freedom is derived from first principles for a driven vertical cantilever beam with a localized mass and symmetric stops. The resulting piecewise-linear dynamical system is smoothed by a…
It is common that the average length of chaotic transients appearing as a consequence of crises in dynamical systems obeys a power low of scaling with the distance from the crisis point. It is, however, only a rough trend; in some cases…
This work explores the dynamic properties of test particles surrounding a distorted, deformed compact object. The astrophysical motivation was to choose such background, which could constitute a more reasonable model of a real situation…
We study a model problem describing vibrational resonance by means of a high-order averaging technique based on so-called word series. With the tech- nique applied here, the tasks of constructing the averaged system and the associ- ated…
As a phenomenon in dynamical systems allowing autonomous switching between stable behaviors, chaotic itinerancy has gained interest in neurorobotics research. In this study, we draw a connection between this phenomenon and the predictive…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
The steady states of two vibrated granular gases separated by an adiabatic piston are investigated. The system exhibits a non-equilibrium phase transition with an spontaneous symmetry breaking. Even if the gases at both sides of the piston…
This paper focuses on the isogeometric vibration analysis of curvilinearly stiffened composite panels. The stiffness matrices and the mass matrices are derived using the first-order shear deformation theory (FSDT). The present method models…
We discuss the appearance of chaos in time-periodic perturbations of reversible vector fields in the plane. We use the normal forms of codimension~$1$ reversible vector fields and discuss the ways a time-dependent periodic forcing term of…
We propose a simple nanostructured pinning array geometry where a rich variety of complex vortex shear banding phenomena can be realized. A single row of pinning sites is removed from a square pinning array. Shear banding effects arise when…
We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or…
The article is devoted to the investigation of the nonlinear effects in a system of the coupled longitudinal-torsional parametric vibrations of a rotating rod. Constructed and investigated mathematical model, based on which we calculated…
Numerical experiments recently discussed in the literature show that identical nonlinear chaotic systems linked by a common noise term (or signal) may synchronize after a finite time. We study the process of synchronization as function of…
When an oscillator switches abruptly between different frequencies, there is some ambiguity in deciding how the system should be modelled at the switch. Here we describe two seemingly natural models of a switch in a simple…
Vibration peaks occurring at rational fractions of the fundamental rotating critical speed, here named Local Resonances, facilitate cracked shaft detection during machine shut-down. A modified Jeffcott-rotor on journal bearings accounting…
We conjecture that chaotic resonance modes in scattering systems are a product of a conditionally invariant measure from classical dynamics and universal exponentially distributed fluctuations. The multifractal structure of the first factor…