Related papers: Complex dynamics in hard oscillators: the influenc…

We study synchronization in large populations of coupled phase oscillators with time-delays, higher order interactions. With each of these effects individually giving rise to bistabiltiy between incoherence and synchronization via a…

Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…

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 study the dynamics of a finite chain of diffusively coupled Lorenz oscillators with periodic boundary conditions. Such rings possess infinitely many fixed states, some of which are observed to be stable. It is shown that there exists a…

The problem of reliability of the dynamics in biological regulatory networks is studied in the framework of a generalized Boolean network model with continuous timing and noise. Using well-known artificial genetic networks such as the…

Microresonators are micron-scale optical systems that confine light using total internal reflection. These optical systems have gained interest in the last two decades due to their compact sizes, unprecedented measurement capabilities, and…

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…

We consider controller design for robust output tracking and disturbance rejection for continuous-time periodic linear systems with periodic reference and disturbance signals. As our main results we present four different controllers: A…

Conditions are provided under which lack of domination of a homoclinic class yields robust heterodimensional cycles. Moreover, so-called viral homoclinic classes are studied. Viral classes have the property of generating copies of…

Oscillations represent a ubiquitous phenomenon in biological systems. The conventional models of biological periodic oscillations are usually proposed as interconnecting transcriptional feedback loops. Some specific proteins function as…

We study an unusual but robust phenomenon that appears in an example system of four coupled phase oscillators. We show that the system can have a robust attractor that responds to a specific detuning between certain pairs of the oscillators…

Regulatory dynamics in biology is often described by continuous rate equations for continuously varying chemical concentrations. Binary discretization of state space and time leads to Boolean dynamics. In the latter, the dynamics has been…

Logical modeling is a powerful tool in biology, offering a system-level understanding of the complex interactions that govern biological processes. A gap that hinders the scalability of logical models is the need to specify the update…

We analyze the complexity of classically simulating continuous-time dynamics of locally interacting quantum spin systems with a constant rate of entanglement breaking noise. We prove that a polynomial time classical algorithm can be used to…

Dynamical processes on time-varying complex networks are key to understanding and modeling a broad variety of processes in socio-technical systems. Here we focus on empirical temporal networks of human proximity and we aim at understanding…

The structure and dynamics of a typical biological system are complex due to strong and inhomogeneous interactions between its constituents. The investigation of such systems with classical mathematical tools, such as differential equations…

A wide range of organisms use circadian clocks to keep internal sense of daily time and regulate their behavior accordingly. Most of these clocks use intracellular genetic networks based on positive and negative regulatory elements. The…

We study the effect of external forcing on the saddle-node bifurcation pattern of interval maps. By replacing fixed points of unperturbed maps by invariant graphs, we obtain direct analogues to the classical result both for random forcing…

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…

We consider a model for substrate-depletion oscillations in genetic systems, based on a stochastic differential equation with a slowly evolving external signal. We show the existence of critical transitions in the system. We apply two…