Related papers: Higher Dimensional Limit Cycles and Coupling Induc…
In our earlier studies, we found the effect of non-conventional synchronization, which is a specific type of nonlinear stable beating in the system of two weakly coupled autogenerators with hard excitation given by generalized van der…
We study synchronization of two dissipatively coupled Van der Pol oscillators in the quantum regime. Due to quantum noise strict frequency locking is absent and is replaced by a crossover from weak to strong frequency entrainment. We…
An overview is given on two representative methods of dynamical reduction known as center-manifold reduction and phase reduction. These theories are presented in a somewhat more unified fashion than the theories in the past. The target…
Phase reduction is a general approach to describe coupled oscillatory units in terms of their phases, assuming that the amplitudes are enslaved. For such a reduction, the coupling should be small, but one also expects the reduction to be…
Canard cycles are periodic orbits that appear as special solutions of fast-slow systems (or singularly perturbed Ordinary Differential Equations). It is well known that canard cycles are difficult to detect, hard to reproduce numerically,…
We experimentally demonstrate the occurrence of various synchronized states in coupled piece-wise linear time-delayed electronic circuits using dynamic environment coupling where the environment has its own intrinsic dynamics via feedback…
A comparative study of the Homotopy Analysis method and an improved Renormalization Group method is presented in the context of the Rayleigh and the Van der Pol equations. Efficient approximate formulae as functions of the nonlinearity…
This paper addresses the perturbation of higher-dimensional non-smooth autonomous differential systems characterized by two zones separated by a codimension-one manifold, with an integral manifold foliated by crossing periodic solutions.…
The synchronization of rhythms is ubiquitous in both natural and engineered systems, and the demand for data-driven analysis is growing. When rhythms arise from limit cycles, phase reduction theory shows that their dynamics are universally…
We develop an analytical framework to study the synchronization of a quantum self-sustained oscillator to an external signal. Our unified description allows us to identify the resource on which quantum synchronization relies, and to compare…
To observe synchronization in a large network of classical or quantum systems demands both excellent control of the interactions between the nodes and very accurate preparation of the initial conditions due to the involved nonlinearities…
We study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of…
We consider a Hamiltonian system of coupled Van der Pol-Duffing(VdPD) oscillators with balanced loss and gain. The system is analyzed perturbatively by using Renormalization Group(RG) techniques as well as Multiple Scale Analysis(MSA). Both…
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.…
We analyse the properties of the synchronisation transition in a many-body system consisting of quantum van der Pol oscillators with all-to-all coupling using a self-consistent mean-field method. We find that the synchronised state, which…
Dynamical systems can be coupled in a manner that is designed to drive the resulting dynamics onto a specified lower dimensional submanifold in the phase space of the combined system. On the submanifold, the variables of the two systems…
Optimization of mutual synchronization between a pair of limit-cycle oscillators with weak symmetric coupling is considered in the framework of the phase reduction theory. By generalizing a previous study on the optimization of…
Self-oscillating systems, described in classical dynamics as limit cycles, are emerging as canonical models for driven dissipative nonequilibrium open quantum systems, and as key elements in quantum technology. We consider a family of…
This paper examines the dynamics of power-electronic inverters in islanded microgrids that are controlled to emulate the dynamics of Van der Pol oscillators. The general strategy of controlling inverters to emulate the behavior of nonlinear…
We report a spectrum of exotic frequency-locked states in a ring of phase oscillators with pure three-body interactions. For identical oscillators, the system hosts a vast multiplicity of stable quantized frequency-locked states without…