Search

The paper is dedicated to the numerical and experimental study of nonlinear oscillations exhibited by the Vilnius chaotic generator. The motivation for the work is defined by the need for a comprehensive analysis of the dynamics of the oscillators being embedded into chaotic communication systems. These generators should provide low-power operation while ensuring the robustness of the chaotic oscillations, insusceptible to parameter variations and noise. The work focuses on the investigation of the dependence of nonlinear dynamics of the Vilnius oscillator on the operating voltage and component parameter changes. The paper shows that the application of the Method of Complete Bifurcation Groups reveals the complex smooth and non-smooth bifurcation structures, forming regions of robust chaotic oscillations. The novel tool—mode transition graph—is presented, allowing the comparison of experimental and numerical results. The paper demonstrates the applicability of the Vilnius oscillator for the generation of robust chaos, and highlights the need for further investigation of the inherent trade-off between energy efficiency and robustness of the obtained oscillations. [ABSTRACT FROM AUTHOR]

An application of the new method of complete bifurcation groups (MCBG) in parametrically excited pendulum systems with several equilibrium positions and with the periodically vibrating point of suspension in both directions is introduced. Construction of complete bifurcation groups is based on the method of stable and unstable periodic regimes continuation on a parameter. Global bifurcation analysis of the parametrically excited pendulum systems with several equilibrium positions allows finding new bifurcation groups with rare attractors and chaotic regimes. [ABSTRACT FROM AUTHOR]

An application of the new method of complete bifurcation groups (MCBG) in parametrically excited pendulum systems with an additional linear restoring moment and with the periodically vibrating point of suspension in both directions is introduced. Behaviour of the driven damped pendulum systems may be complex and with unexpected phenomena. Recent efforts in nonlinear dynamics show, that rare attractors (RA) have been found in all typical nonlinear models. Construction of complete bifurcation groups is based on the method of stable and unstable periodic regimes continuation on a parameter. This method is based on the ideas of Poincaré, Birkhoff, Andronov and others [6]. Global bifurcation analysis of the parametric pendulum systems allows to find new bifurcation groups, rare attractors and chaotic regimes. All results were obtained numerically, using our software. [ABSTRACT FROM AUTHOR]

This paper devoted to application of the new method of complete bifurcation groups (MCBG), which shows very good results in single-degree-of-freedom tasks, for global bifurcation analysis of systems with two degrees-offreedom on example of two-mass chain system with symmetrical elastic characteristic with two potential wells between masses. It is shown, that using of the MCBG allows to implement global bifurcation analysis of nonlinear oscillators with 2 DOF, and to find new nonlinear effects, bifurcation groups, and unknown before periodic and chaotic regimes. [ABSTRACT FROM AUTHOR]