We investigate the dynamics of the nonlinear DDE (delay-differential equation) \(\frac{\hbox {d}^2x}{\hbox {d}t^2}(t)+x(t-T)+x(t)^3=0\), where T is the delay. For \(T=0\), this system is conservative and exhibits no limit cycles. For \(T>0\), no matter how small T is, an infinite number of limit cycles exist, their amplitudes going to infinity in the limit as T approaches zero. We ...

Modeling and control of diabetes mellitus (DM) are difficult due to the highly nonlinear attitude, time-delay effects, the impulse kind input signals and the lack of continuously available blood glucose (BG) level to be regulated. Regarding the mentioned problems, identification of DM model is crucial. Furthermore, due to the lack of information about the internal states (which ...

Brand-new equations which can be regarded as modifications of Khokhlov–Zabolotskaya–Kuznetsov or Ostrovsky–Vakhnenko equations are suggested. These equations are quite general in that they describe the nonlinear wave dynamics in media with modular nonlinearity. Such media exist among composites, meta-materials, inhomogeneous and multiphase systems. These new models are interesting ...

The article presents authors’ recent results on nonlinear lateral stability of rail vehicles in a curved track. The theories of self-exciting vibrations and bifurcation are the key elements here. The general objective is presentation of extended use of the earlier worked out authors’ method to more complex rail vehicle models. Two 4-axle vehicle models were created. The first one ...

This paper studies the dynamics of the vibro-impact capsule systems with one-sided and two-sided soft constraints under variations of various system and control parameters, including mass ratio, stiffness ratio, gap of contact, and amplitude and frequency of external excitation. The aim of this study is to optimise the progression speed and energy consumption of the capsule and ...

This paper presents novel approach to the task of control performance assessment. Proposed approach does not require any a priori knowledge on process model and uses control error time series data using nonlinear dynamical fractal persistence measures. Notion of the rescaled range R/S plots with estimation of Hurst exponent is applied. Crossover phenomenon is observed in data being ...

The stability and convergence of state, disturbance and parametric estimates of a robot have been analyzed using the Lyapunov method in the existing literature. In this paper, we analyze the problem of stochastic stability and also prove some results regarding behavior of statistically averaged Lyapunov energy function in the presence of jerk noise modeled as the sum of independent ...

In this paper, we consider a pulse dynamics in nonlinear optics (fiber-optic communications) in the presence of both self-steepening and septic nonlinear effects. Propagating profiles of the septic derivative nonlinear Schrödinger model which are isolated via coupled integrable invariants of motion, that admits exact solution, are investigated by a method of dynamical systems. By ...

The study discusses the problem of determining vertical displacements of a riser’s ends, which, despite its horizontal displacements induced by waves, mitigate stresses. A spatial model of riser dynamics is presented that considers the geometric nonlinearity due to large deflections. The Rigid Finite Element Method was used for riser discretisation. Analyses are reported that ...

Modeling and analysis of complex dynamical systems can be effectively performed using multibody system (MBS) simulation software. Many modern MBS packages are able to efficiently and reliably handle rigid and flexible bodies, often offering a wide choice of different formulations. Despite many advances in modeling of flexible systems, the most widely used formulation remains the ...

In this paper, two different concepts of multiple task motion planning algorithm for nonholonomic systems are considered. The egalitarian approach treats all the tasks equivalently and tries to solve all the tasks simultaneously. In contrast, the prioritarian approach arranges the tasks with decreasing priorities in such a way that the solution of the lower order task should not ...

This work concerns the control of multistability in a vibro-impact capsule system driven by a harmonic excitation. The capsule is able to move forward and backward in a rectilinear direction, and the main objective of this work is to control such motion in the presence of multiple coexisting periodic solutions. A position feedback controller is employed in this study, and our ...

In this paper, we analyze the dynamics of tuned mass dampers with inerters. In the beginning, we describe the influence of inertance value with respect to the overall mass of the damping device. For further analysis, we pick three practically significant cases—each corresponding to different composition of tuned mass damper inertia. Then, we focus on the effects caused by different ...

We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for computing the solution when using a variety of analytical approaches. In the case where this reduction is possible, we employ differential elimination ...

In order to obtain an isolator with low resonance amplitude as well as good isolation performance at high frequencies, this paper explores the usage of nonlinear stiffness elements to improve the transmissibility efficiency of a sufficient linear damped vibration isolator featured with the Zener model. More specifically, we intend to improve its original poor high-frequency ...

Mandelbrot and Julia sets are examples of fractal patterns generated in the complex plane. In the literature, we can find many generalizations of those sets. One of such generalizations is the use of switching process. In this paper, we introduce some switching processes to another type of complex fractals, namely polynomiographs. Polynomiograph is an image presenting the ...

The transverse vibration of an elastic disc, excited by a preloaded mass–damper–spring slider dragged around on the disc surface at a constant rotating speed and undergoing in-plane stick–slip oscillation due to friction, is studied. As the vertical vibration of the slider grows at certain conditions, it can separate from the disc and then reattach to the disc. Numerical simulation ...

The new generations of compact high output power-to-weight ratio internal combustion engines generate broadband torsional oscillations, transmitted to lightly damped drivetrain systems. A novel approach to mitigate these untoward vibrations can be the use of nonlinear absorbers. These act as Nonlinear Energy Sinks (NESs). The NES is coupled to the primary (drivetrain) structure, ...