Related papers: Miquel dynamics for circle patterns

Limit cycle oscillations are phenomena arising in nonlinear dynamical systems and characterized by periodic, locally-stable, and self-sustained state trajectories. Systems controlled in a closed loop along a periodic trajectory can also be…

We investigate a new two-dimensional compressible Navier-Stokes hydrodynamic model design to explain and study large scale ice swirls formation at the surface of the ocean. The linearized model generates a basis of Bessel solutions from…

We formulate a geometric measurement theory of dynamical classical systems possessing both continuous and discrete degrees of freedom. The approach is covariant with respect to choices of clocks and canonically incorporates laboratories.…

In four-dimensional symplectic maps complex instability of periodic orbits is possible, which cannot occur in the two-dimensional case. We investigate the transition from stable to complex unstable dynamics of a fixed point under parameter…

Bifurcations are one of the most remarkable features of dynamical systems. Corral et al. [Sci. Rep. 8(11783), 2018] showed the existence of scaling laws describing the transient (finite-time) dynamics in discrete dynamical systems close to…

Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…

We consider the model of a point-vortex under a periodic perturbation and give sufficient conditions for the existence of generalized quasi-periodic solutions with rotation number. The proof uses Aubry-Mather theory to obtain the existence…

A numerical technique used to solve boundary value problems is modified to find periodic steady-state solutions of nonautonomous dynamical systems. The technique uses a matrix representation of the time derivative obtained through…

We study the rotational structures of aperiodic tilings in Euclidean space of arbitrary dimension using topological methods. Classical topological approaches to the study of aperiodic patterns have largely concentrated just on translational…

We generalize the Vicsek model to describe the collective behaviour of polar circle swimmers with local alignment interactions. While the phase transition leading to collective motion in 2D (flocking) occurs at the same interaction to noise…

Patterns on curved surfaces are ubiquitous, yet the influence of surface geometry on pattern dynamics remains elusive. We recently reported a new mechanism of pattern propagation in which a static pattern on a flat plane becomes a…

This paper is the forth part of our series of work, is devoted to the analysis on the multiscales and cascade aspects of the statistical theory of isotropic turbulence based on the new Sedov-type solution. In this paper, we use the explicit…

Many practical approximations in physics and engineering invoke a relatively long physical domain with a relatively thin cross-section. In this scenario we typically expect the system to have structures that vary slowly in the long…

The long-time behaviour of many dynamical systems may be effectively predicted by a low-dimensional model that describes the evolution of a reduced set of variables. We consider the question of how to equip such a low-dimensional model with…

A heterodimensional cycle is an invariant set of a dynamical system consisting of two hyperbolic periodic orbits with different dimensions of their unstable manifolds and a pair of orbits that connect them. For systems which are at least…

The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…

We present a construction of new invariant sets for fibred polynomial dynamics with base an irrational rotation over the unit circle, called multi-curves. Furthermore, the local dynamical theory for attracting invariant curves is extended…

In this article we consider two dynamical systems: the McMillan sextupole and octupole integrable mappings originally introduced by Edwin McMillan; the second one is also known as canonical McMillan map. Both of them are simplest symmetric…

We present a simple dynamical systems model for the effect of invisible space dimensions on the visible ones. There are three premises. A: Orbits consist of flows of probabilities [P].which is the case in the setting of quantum mechanics.…

In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic up in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a…