Related papers: Describing dynamics of driven multistable oscillat…
Phase response curves are important for analysis and modeling of oscillatory dynamics in various applications, particularly in neuroscience. Standard experimental technique for determining them requires isolation of the system and…
An effective description of a general class of stochastic phase oscillators is presented. For this, the effective phase velocity is defined either by invariant probability density or via first passage times. While the first approach…
We consider the dynamical properties of a simple model of vibrational surface modes. We obtain the exact spectrum of surface excitations and discuss their dynamical features. In addition to the usually discussed localized and oscillatory…
Oscillator models are central to the study of system properties such as entrainment or synchronization. Due to their nonlinear nature, few system-theoretic tools exist to analyze those models. The paper develops a sensitivity analysis for…
Large systems of coupled oscillators subjected to a periodic external drive occur in many situations in physics and biology. Here the simple, paradigmatic case of equal-strength, all-to-all sine-coupling of phase oscillators subject to a…
Sensitivity analysis is a classical and fundamental tool to evaluate the role of a given parameter in a given system characteristic. Because the phase response curve is a fundamental input--output characteristic of oscillators, we developed…
Phase response curve (PRC) is an extremely useful tool for studying the response of oscillatory systems, e.g. neurons, to sparse or weak stimulation. Here we develop a framework for studying the response to a series of pulses which are…
We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a perturbed system, we construct numerically the equation for…
The dynamics of a non-autonomous oscillator in which the phase and frequency of the external force depend on the dynamical variable is studied. Such a control of the phase and frequency of the external force leads to the appearance of…
This study investigates the existence and stability of limit cycles resulting from self-excited oscillations in linear multi-degree-of-freedom systems subjected to discontinuous, state-dependent forcing. Using the method of averaging and…
Multiplicity of phase states within frequency locked bands in periodically forced oscillatory systems may give rise to front structures separating states with different phases. A new front instability is found within bands where…
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…
We investigate numerically the dynamics of traveling clusters in systems of phase oscillators, some of which possess positive couplings and others negative couplings. The phase distribution, speed of traveling, and average separation…
We propose a model that describes phase transition including metastable phases present in the van der Waals Equation of State (EoS). We introduce a dynamical system that is able to depict the mass transfer between two phases, for which…
The periodic modulation of an oscillator's frequency can lead to so-called parametric oscillations at half the driving frequency, which display bistability between two states whose phases differ by \pi. Such phase-locking bistability is at…
We analyze the rates of noise-induced transitions between period-two attractors. The model investigated is an underdamped oscillator parametrically driven by a field at nearly twice the oscillator eigenfrequency. The activation energy of…
We address two aspects of the dynamics of the forced Duffing oscillator which are relevant to the technology of micromechanical devices and, at the same time, have intrinsic significance to the field of nonlinear oscillating systems. First,…
It is understood that congestion in traffic can be interpreted in terms of the instability of the equation of dynamic motion. The evolution of a traffic system from an unstable or metastable state to a globally stable state bears a strong…
The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine…
We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest…