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Complex dynamical systems may exhibit multiple steady states, including time-periodic limit cycles, where the final trajectory depends on initial conditions. With tuning of parameters, limit cycles can proliferate or merge at an exceptional…

In this article, we present an analysis of the effects of nonlinear circuits on bistable vibration energy harvesters. We begin by introducing an analytical model for bistable vibration energy harvesters and demonstrate that the impact of…

We consider a massive particle driven with a constant force in a periodic potential and subjected to a dissipative friction. As a function of the drive and damping, the phase diagram of this paradigmatic model is well known to present a…

A delayed feedback control framework for stabilizing unstable periodic orbits of linear periodic time-varying systems is proposed. In this framework, act-and-wait approach is utilized for switching a delayed feedback controller on and off…

Nonreciprocal entanglement, characterized by inherently robust operation, is a cornerstone for quantum information processing and communications. However, it remains a great challenge to achieve nonreciprocal entanglement characterized by…

The dynamical backaction from a periodically driven optical or microwave cavity can reduce the damping of a mechanical resonator, leading to parametric instability accompanied by self-sustained oscillations. Fundamentally, the driving…

Topological phase transitions can be remarkably induced purely by manipulating gain and loss mechanisms, offering a novel approach to engineering topological properties. Recent theoretical studies have revealed gain-loss-induced topological…

Weakly coupled limit cycle oscillators can be reduced into a system of weakly coupled phase models. These phase models are helpful to analyze the synchronization phenomena. For example, a phase model of two oscillators has a one-dimensional…

The coupled electron-nuclear spin system in an InGaAs semiconductor as testbed of nonlinear dynamics can develop auto-oscillations, resembling time-crystalline behavior, when continuously excited by a circularly polarized laser. We expose…

We examine a strange chaotic attractor and its unstable periodic orbits in case of one degree of freedom nonlinear oscillator with non symmetric potential. We propose an efficient method of chaos control stabilizing these orbits by a…

An optomechanical oscillator undergoes a Hopf bifurcation that connects two dynamical regimes with different information-processing capabilities: thermal Brownian motion and coherent self-sustained oscillation. Below threshold, the…

Additive noise is known to produce counter-intuitive behaviors in nonlinear dynamical systems. Previously, it was shown that systems with a deterministic limit cycle can display bistable switching between metastable states in the presence…

Controlling nonlinear effects in micro- and nano-electro-mechanical systems is essential for unlocking their full potential in sensing, signal processing, and frequency control. In this study, we develop a voltage-dependent Hamiltonian…

We propose a simple and new unified method to achieve lag, complete and anticipatory synchronizations in coupled nonlinear systems. It can be considered as an alternative to the subsystem and intentional parameter mismatch methods. This…

We investigate an oscillator linearly coupled with a one-dimensional Ising system. The coupling gives rise to drastic changes both in the oscillator statics and dynamics. Firstly, there appears a second order phase transition, with the…

Brain dynamics can exhibit narrow-band nonlinear oscillations and multistability. For a subset of disorders of consciousness and motor control, we hypothesize that some symptoms originate from the inability to spontaneously transition from…

We show that the nonlinear response of a driven circuit quantum electrodynamics setup displays antiresonant multiphoton transitions, as recently observed in a transmon qubit device. By including photon leaking, we explain the lineshape by a…

We show that optomechanical quantum systems can undergo dissipative phase transitions within the limit of small nonlinear interaction and strong external drive. In such a defined thermodynamical limit, the nonlinear interaction stabilizes…

Bistable mechanisms are prevalent across a broad spectrum of applications due to their ability to maintain two distinct stable states. Their energy consumption is predominantly confined to the process of state transitions, thereby enhancing…

We consider the problem of stochastic exit from a planar domain, whose boundary is an unstable periodic orbit, and which contains a stable periodic orbit. This problem arises when investigating the distribution of noise-induced phase slips…