Related papers: Iterated maps for clarinet-like systems
A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during…
The phase diagrams and transitions of nonequilibrium systems with multiplicative noise are studied theoretically. We show the existence of both strong and weak-coupling critical behavior, of two distinct active phases, and of a nonzero…
Discrete time-translation symmetry breaking can be observed in periodically-driven systems oscillating at a fraction of the frequency of the driving force. However, with the exception of the parametric instability in period-doubling,…
Periodic forcing of nonlinear oscillators leads to a large number of dynamic behaviors. The coupling of the cell-cycle to the circadian clock provides a biological realization of such forcing. Using high throughput single-cell microscopy,…
Previous studies have shown that noise can induce coherence resonance in some nonlinear dynamical systems close to a bifurcation of a periodic motion, such as in excitable systems. We demonstrate that coherence resonance can be observed in…
Limit cycles are self-sustained, closed trajectories in phase space representing (un)-stable, periodic behavior in nonlinear dynamical systems. They underpin diverse natural phenomena, from neuronal firing patterns to engineering…
We show the possibility of controlling the dynamical behavior of a single fiber ring (SFR) resonator system with the fiber being an amplified (gain) channel and the ring being attenuated (loss) nonlinear dielectric medium. Our model is…
In this paper we address the numerical solution of nonlinear ill-posed systems by iterative regularization methods in the classes of Levenberg-Marquardt, trust-region and adaptive quadratic regularization procedures. Both with exact and…
Chemical oscillation is an interesting nonlinear dynamical phenomenon which arises due to complex stability condition of the steady state of a reaction far away from equilibrium which is usually characterised by a periodic attractor or a…
In the bi-dimensional parameter space of driven oscillators, shrimp-shaped periodic windows are immersed in chaotic regions. For two of these oscillators, namely, Duffing and Josephson junction, we show that a weak harmonic perturbation…
Systems with nonreciprocal interactions generically display time-dependent states. These are routinely observed in finite systems, from neuroscience to active matter, in which globally ordered oscillations exist. However, the stability of…
We investigate the processes of synchronization and phase ordering in a system of globally coupled maps possessing bistable, chaotic local dynamics. The stability boundaries of the synchronized states are determined on the space of…
The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…
We investigate the spatio-temporal dynamics of coupled chaotic systems with nonlocal interactions, where each element is coupled to its nearest neighbors within a finite range. Depending upon the coupling strength and coupling radius, we…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
An optoelectronic oscillator exhibiting a large delay in its feedback loop is studied both experimentally and theoretically. We show that multiple square-wave oscillations may coexist for the same values of the parameters…
Similar activity patterns may arise from model neural networks with distinct coupling properties and individual unit dynamics. These similar patterns may, however, respond differently to parameter variations and, specifically, to tuning of…
When dynamical systems that produce rhythmic behaviors operate within hard limits, they may exhibit limit cycles with sliding components, that is, closed isolated periodic orbits that make and break contact with a constraint surface.…
We consider the orientational instabilities, both homogeneous and spatially periodic, developing in a nematic liquid crystal under rectilinear oscillatory Couette flow for director alignment perpendicular to the flow plane. Using numerical…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…