This study presents modelling and analysis of a new magneto-mechanical (MM) oscillator (Wiercigroch et al., 2020), which pays special attention to mechanical magnetic nonlinearities for large amplitude responses. The is comprised box structure made two parallel leaf springs with one end fixed the other clamped proof mass, an electromagnetic actuator. A solenoid permanent magnet are main parts a...

In this paper, we discuss fundamentals for the design of a source of chaotic signals based on a blocking oscillator circuit. We study a modification of a well-known circuit of blocking oscillator which leads to the onset of chaotic oscillations. The output signal of such chaotic oscillator is a series of short term pulses characterized by chaotic fluctuations of time intervals between pulses. S...

In the present paper, a new 2-D Van der Polstructural oscillator model is introduced for the vortex induced vibrations of circular cylinders.The main purpose of this task is to control the recently introduced model by means of modern control definitions in state space. In order to control the system, the whole model is linearized about its equilibrium point by deriving state-space matrices. The...

The current paper focuses on some analytical techniques to solve the non-linear Duffing oscillator with large nonlinearity. Four different methods have been applied for solution of the equation of motion; the variational iteration method, He’s parameter expanding method, parameterized perturbation method, and the homotopy perturbation method. The results reveal that approxim...

The work is devoted to the systematic research of the periodic, quasi-periodic or chaotic oscillations and the coexistence in the nonlinear Duffing-van der Pol type dynamical systems describing processes and phenomena in nature or engineering. The achieved result is the elaboration of the basic theory for searching nonlinear effects based on the concepts of periodic skeletons, bifurcation theor...

The exact solution of the anti-symmetric quadratic truly nonlinear oscillator is derived from the first integral of the nonlinear differential equation which governs the behaviour of this oscillator. This exact solution is expressed as a piecewise function including Jacobi elliptic cosine functions. The Fourier series expansion of the exact solution is also analyzed and its coefficients are com...

The nonlinear two-degree-of-freedom system under consideration consists of the linear oscillator with a relatively big mass, which is an approximation of some continuous elastic system, and of the vibro-impact oscillator with a relatively small mass, which is an absorber of the linear system vibrations. Analysis of nonlinear normal vibration modes shows that a stable localized vibration mode, w...

In this paper, we prove that the modified PainlevéInce (PI) equation, the force-free Duffing nonlinear type oscillator (DO) and the Lotka-Volterra (LV) nonlinear ordinary differential equation ODEs can be solved in general parametric form. The developed mathematical methodology and the extracted results, being expressed by way of new theorems including admissible functional transformations and ...

An optoelectronic nonlinear delay oscillator seeded by a pulsed laser source is used to experimentally demonstrate a new transition scenario for the general class of delay differential dynamics, from continuous to discrete time behavior. This transition scenario differs from the singular limit map, or adiabatic approximation model that is usually considered. The transition from the map to the f...

We examine the Melnikov criterion for a global homoclinic bifurcation and a possible transition to chaos in case of a single degree of freedom nonlinear oscillator with a symmetric double well nonlinear potential. The system was subjected simultaneously to parametric periodic forcing and self excitation via negative damping term. Detailed numerical studies confirm the analytical predictions and...