Related papers: Numerical phase reduction beyond the first order a…
In view of the current availability and variety of measured data, there is an increasing demand for powerful signal processing tools that can cope successfully with the associated problems that often arise when data are being analysed. In…
We numerically study a directed small-world network consisting of attractively coupled, identical phase oscillators. While complete synchronization is always stable, it is not always reachable from random initial conditions. Depending on…
A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show…
Circular variables such as phase or orientation have received considerable attention throughout the scientific and engineering communities and have recently been quite prominent in the field of neuroscience. While many analytic techniques…
Biological systems can rely on collective formation of a metachronal wave in an ensemble of oscillators for locomotion and for fluid transport. We consider one-dimensional chains of phase oscillators with nearest neighbor interactions,…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…
An important aspect of the recently introduced transient uncoupling scheme is that it induces synchronization for large values of coupling strength at which the coupled chaotic systems resist synchronization when continu- ously coupled.…
We study an active random walker model in which a particle's motion is determined by a self-generated field. The field encodes information about the particle's path history. This leads to either self-attractive or self-repelling behavior.…
We derive and analyze numerical methods for underdamped (kinetic) Langevin dynamics in a domain with elastic reflection at the boundary. First-order approximations are based on an Euler-type scheme incorporating collision-handling at the…
Self-sustaining nonlinear oscillators of practically any type can function as latches and registers if Boolean logic states are represented physically as the phase of oscillatory signals. Combinational operations on such phase-encoded logic…
Phase retrieval consists in the recovery of a complex-valued signal from intensity-only measurements. As it pervades a broad variety of applications, many researchers have striven to develop phase-retrieval algorithms. Classical approaches…
We propose a method for optimizing mutual coupling functions to achieve fast and global synchronization between a pair of weakly coupled limit-cycle oscillators. Our method is based on phase reduction that provides a concise low-dimensional…
For a system of coupled identical phase oscillators with full permutation symmetry, any broken symmetries in dynamical behaviour must come from spontaneous symmetry breaking, i.e. from the nonlinear dynamics of the system. The dynamics of…
We establish a new approach to calculating spectral statistics in disordered conductors, by considering how energy levels move in response to changes in the impurity potential. We use this fictitious dynamics to calculate the spectral form…
In silico models of cardiac electromechanics couple together mathematical models describing different physics. One instance is represented by the model describing the generation of active force, coupled with the one of tissue mechanics. For…
We introduce a prototype model for globally-coupled oscillators in which each element is given an oscillation frequency and a preferential oscillation direction (polarization), both randomly distributed. We found two collective transitions:…
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent…
The numerical integration of phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties of the solution such as energy dissipation and maximum principle. Although the theory of energy…
The quantum dynamics of two weakly coupled nonlinear oscillators is analytically and numerically investigated in the context of nonlinear dissipation. The latter facilitates the creation and preservation of non-classical steady states.…