ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


Attractors of smale–williams type in periodically kicked model systems

Examples of model non­autonomous systems are constructed and studied possessing hyperbolic attractors of Smale–Williams type in their stroboscopic maps. The dynamics is determined by application of a periodic sequence of kicks, in such way that on one period of the external driving the angular coordinate, or the phase of oscillations, behaves in accordance with an expanding circle map with chaotic dynamics.

Rotational dynamics in the system of two coupled pendulums

We consider dynamics in a pair of nonlinearly coupled pendulums. With existence of dissipation and constant torque such system can demonstrate in-phase periodical rotation in addition to the stable state. We have shown in numerical simulations that such in- phase rotation becomes unstable at certain values of coupling strength. In the limit of small dissipation we have created an asymptotic theory that explains instability of the in-phase cycle. Found analytical equations for coupling strength values corresponding to the boundaries of the instability area.

The dynamics of two nonlinearly coupled oscillators

In this paper the dynamics of two elastically coupled pendulums is studied. The pendulums oscillate under the influence of external rotational moments, their masses are considered to be equal. The current work is motivated by multiple applications in physics and biology that the model has. Due to the fact that most of the previous studies focused on similar systems of higher order, we believe that the current research can serve as a basis for understanding the functioning of more complex oscillatory ensembles.