# Nonlinear Dynamics

## List of Papers (Total 159)

#### Periodic solution of a pest management Gompertz model with impulsive state feedback control

In this paper, a new model with two state impulses is proposed for pest management. According to different thresholds, an integrated strategy of pest management is considered, that is to say if the density of the pest population reaches the lower threshold $h_1$ at which pests cause slight damage to the forest, biological control (releasing natural enemy) will be taken to...

#### Robust fault-tolerant control for flexible spacecraft against partial actuator failures

In this paper, we present a robust fault-tolerant control scheme to achieve attitude control of flexible spacecraft with disturbances and actuator failures. It is shown that the control algorithms are not only attenuate exogenous bounded disturbances with attenuation level, but also able to tolerate partial loss of actuator effectiveness. The proposed controller design is simple...

#### Adaptive control of rotary inverted pendulum system with time-varying uncertainties

In this paper, an adaptive controller is proposed to balance a rotary inverted pendulum with time-varying uncertainties. The goal of the control is to bring the pendulum close to the upright position regardless of the various uncertainties and disturbances. Its underactuated dynamics is first decoupled by Olfati’s transformation into a cascade form, and then an adaptive...

#### Resonance solitons produced by azimuthal modulation in self-focusing and self-defocusing materials

We demonstrate azimuthally modulated resonance scalar and vector solitons in self-focusing and self-defocusing materials. They are constructed by selecting appropriately self-consistency and resonance conditions in a coupled system of multicomponent nonlinear Schrödinger equations. In the case with zero modulation depth, it was found that the larger the topological charge, the...

#### Dynamics of axially accelerating beams with multiple supports

This study represents the transverse vibrations of an axially accelerating Euler–Bernoulli beam resting on multiple simple supports. This is one of the examples of a system experiencing Coriolis acceleration component that renders such systems gyroscopic. A small harmonic variation with a constant mean value for the axial velocity is assumed in the problem. The immovable supports...

#### Amplitude control approach for chaotic signals

A general approach based on the introduction of a control function for constructing amplitude-controllable chaotic systems with quadratic nonlinearities is discussed in this paper. We consider three control regimes where the control functions are applied to different coefficients of the quadratic terms in a dynamical system. The approach is illustrated using the Lorenz system as...

#### Special Lie symmetry and Hojman conserved quantity of Appell equations for a Chetaev nonholonomic system

A special Lie symmetry and Hojman conserved quantity of the Appell equations for a Chetaev nonholonomic system are studied. The differential equations of motion and Appell equations of the Chetaev nonholonomic system are established. Under the special Lie symmetry group transformations in which the time is invariable, the determining equation of the special Lie symmetry of the...

#### Application of Hénon method in numerical estimation of the stick–slip transitions existing in Filippov-type discontinuous dynamical systems with dry friction

Accuracy of numerical modeling of any discontinuous dynamical system plays an important role in the proper use of the tools applied for its analysis. No less important in this matter is the numerical estimation of the phase trajectories, bifurcation diagrams, and Lyapunov exponents. This paper meets these expectations presenting application of Hénon’s method to obtain good...

#### Lie symmetry and approximate Hojman conserved quantity of Appell equations for a weakly nonholonomic system

For a weakly nonholonomic system, the Lie symmetry and approximate Hojman conserved quantity of Appell equations are studied. Based on the Appell equations for a weakly nonholonomic system under special infinitesimal transformations of a group in which the time is invariable, the definition of the Lie symmetry of the weakly nonholonomic system and its first-degree approximate...

#### Dynamic analysis of a simply supported beam resting on a nonlinear elastic foundation under compressive axial load using nonlinear normal modes techniques under three-to-one internal resonance condition

In this paper, the Nonlinear Normal Modes (NNMs) analysis for the case of three-to-one (3:1) internal resonance of a slender simply supported beam in presence of compressive axial load resting on a nonlinear elastic foundation is studied. Using the Euler–Bernoulli beam model, the governing nonlinear PDE of the beam’s transverse vibration and also its associated boundary...

#### A divide and conquer algorithm for constrained multibody system dynamics based on augmented Lagrangian method with projections-based error correction

This paper presents a new parallel algorithm for dynamics simulation of general multibody systems. The developed formulations are iterative and possess divide and conquer structure. The constraints equations are imposed at the acceleration level. Augmented Lagrangian methods with mass-orthogonal projections are used to prevent from constraint violation errors. The proposed...

#### Solving systems of nonlinear difference equations by the multiple scales perturbation method

In this paper, we apply an improved version of the multiple scales perturbation method to a system of weakly nonlinear, regularly perturbed ordinary difference equations. Such systems arise as a result of the discretization of a system of nonlinear differential equations, or as a result in the stability analysis of nonlinear oscillations. In our procedure, asymptotic...

#### Pattern formation of an epidemic model with diffusion

One subject of spatial epidemiology is spatial variation in disease risk or incidence. The spread of epidemics can result in strong spatial patterns of such risk or incidence: for example, pathogen dispersal might be highly localized, vectors or reservoirs for pathogens might be spatially restricted, or susceptible hosts might be clumped. Here, spatial pattern of an epidemic...

#### The largest transversal Lyapunov exponent and master stability function from the perturbation vector and its derivative dot product (TLEVDP)

The behavior of systems of coupled nonlinear oscillators and, connected with it, the synchronization phenomena are of significant interest in many areas of science. One of the most important problems in this field is the stability of the synchronous state. The most often applied tool which allows one to quantify this stability is the largest Transversal Lyapunov Exponent (TLE...

#### Nonlinear dynamics of a regenerative cutting process

We examine the regenerative cutting process by using a single degree of freedom nonsmooth model with a friction component and a time delay term. Instead of the standard Lyapunov exponent calculations, we propose a statistical 0-1 test analysis for chaos detection. This approach reveals the nature of the cutting process signaling regular or chaotic dynamics. For the investigated...

#### Transition to chaos and escape phenomenon in two-degrees-of-freedom oscillator with a kinematic excitation

We study the dynamics of a two-degrees-of-freedom (two-DOF) nonlinear oscillator representing a quarter-car model excited by a road roughness profile. Modeling the road profile by means of a harmonic function, we derive the Melnikov criterion for a system transition to chaos or escape. The analytically obtained estimations are confirmed by numerical simulations. To analyze the...