Hyperchaos and bifurcations in a driven Van der Pol–Duffing oscillator circuit

We investigate the dynamics of a driven Van der Pol–Duffing oscillator circuit and show the existence of higher-dimensional chaotic orbits (or hyperchaos), transient chaos, strange-nonchaotic attractors, as well as quasiperiodic orbits born from Hopf bifurcating orbits. By computing all the Lyapunov exponent spectra, scanning a wide range of the driving frequency and driving amplitude parameter space, we explore in two-parameter space the regimes of different dynamical behaviours

Nonlinear Dynamics of Inverted Pendulum Driven by Airflow

A nonlinear model of inverted pendulum that exhibit unbounded single well / 6 potential is described. The complete equation for one-dimensional wind-induced sway is derived. The harmonic balance method along with Melnikov theory are used to seek the effects of aerodynamic drag forces on the amplitude of vibration, on the structure failure, and on the appearance of horseshoes chaos. Numerical simulations have been performed to confirm analytical investigation

Collective dynamics of a network of ratchets coupled via a stochastic dynamical environment

We investigate the collective dynamics of a network of inertia particles diffusing in a ratchet potential and interacting indirectly through their stochastic dynamical environment. We obtain analytically the condition for the existence of a stable collective state, and we show that the number N of particles in the network, and the strength k of their interaction with the environment, play key roles in synchronization and transport processes. Synchronization is preceded by symmetry-breaking associated with double-resonance oscillations and is shown to be strongly dependent on the network size: convergence to the synchronization manifold occurs much faster with a large network. For small networks, increasing the noise level enhances synchronization in the weakly coupled regime, while particles in a large network are weakly synchronized. Similarly, in the strongly coupled regime, particles in a small network are weakly synchronized; whereas the synchronization is strong and robust against noise when the network-size is large. Small and moderate networks maximize and stabilize efficient transport. Although the dynamics for larger networks is highly correlated, the transport current is erratic. DOI: 10.1103/PhysRevE.87.02291

Multiresonance and enhanced synchronization in stochastically coupled ratchets.

We investigate the dynamics and synchronization of two inertia ratchets interacting indirectly through a stochastic dynamical environment. We examine resonant oscillations in their synchronous and asynchronous modes; and we determine the effects of the interaction with the environment on the system's response and synchronization. We show the occurrence of noise-induced multiresonance and noise-enhanced synchronization emerging from the ratchets' interaction with the noisy environment. The simultaneous quenching of the chaotic regimes, and the domain of gain parameters for efficient control, are identified. It is shown that optimal transport can be achieved, implying that an inertia ratchet can take advantage of its noisy environment to enhance its rich dynamical and transport properties

Dynamical changes from harmonic vibrations of a limited power supply driving a Duffing oscillator

The harmonic oscillations of a Duffing oscillator driven by a limited power supply are investigated as a function of the alternative strength of the rotor. The semi-trivial and non-trivial solutions are derived. We examine the stability of these solutions and then explore the complex behaviors associated with the bifurcations sequences. Interestingly, a 3D diagram provides a global view of the effects of alternate strength on the appearance of chaos and hyperchaos on the system.CNPqCNPqAcademic of Science for the Developing World (TWAS)Academic of Science for the Developing World (TWAS

Synchronization enhancement via an oscillatory bath in a network of self-excited cells

The possibility of using a dynamic environment to achieve and optimize phase synchronization in a network of self-excited cells with free-end boundary conditions is addressed in this paper. The dynamic environment is an oscillatory bath coupled linearly to a network of four cells. The boundaries of the stable solutions of the dynamical states as well as the ranges of coupling parameters leading to stability and instability of synchronization are determined. Numerical simulations are used to check the accuracy and to complement the result obtained from analytical treatment. The robustness of synchronization strategy is tested using a local and global injection of Gaussian white noise in the network. The control gain parameter of the bath coupling can modulate the occurrence of synchronization in the network without prior requirement of direct coupling among all the cells. The process of synchronization obtained through local injection is independent of the node at which noise is injected into the system. As compared to local injection, the global injection scheme increases the range of noise amplitude for which synchronization occurs in the network.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq