Related papers: Exotic Bifurcations Inspired by Walking Droplet Dy…
We analyse three codimension-two bifurcations occurring in nonsmooth systems, when a non-hyperbolic cycle (fold, flip, and Neimark-Sacker cases, both in continuous- and discrete-time) interacts with one of the discontinuity boundaries…
We study the dynamics of nonlinear random walks on complex networks. We investigate the role and effect of directed network topologies on long-term dynamics. While a period-doubling bifurcation to alternating patterns occurs at a critical…
In diverse physical systems stable oscillatory solutions devolve into more complicated dynamical behaviour through border-collision bifurcations. Mathematically these occur when a stable fixed point of a piecewise-smooth map collides with a…
Oscillating shape motion of a freely falling water droplet has long fascinated and inspired scientists. We propose dynamic non-linear equations for closed, two dimensional surfaces in gravity and apply it to analyze shape dynamics of freely…
Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding…
The article summarizes the studies of wave fields in structured non-equilibrium media describing by means of nonlocal hydrodynamic models. Due to the symmetry properties of models, we derived the invariant wave solutions satisfying…
We study the bifurcations and the chaotic behaviour of a periodically forced double-well Duffing oscillator coupled to a single-well Duffing oscillator. Using the amplitude and the frequency of the driving force as control parameters, we…
Stability and bifurcation properties of one-dimensional discrete dynamical systems with positivity, which are derived from continuous ones by tropical discretization, are studied. The discretized time interval is introduced as a bifurcation…
We experimentally investigate the dynamics of synthetic active particles composed of gravitationally bouncing, superwalking droplets confined within an annular fluid bath. Driven by a topologically pumping dual-frequency waveform, the…
We prove the existence of an unbounded connected branch of nontrivial homoclinic trajectories of a family of discrete nonautonomous asymptotically hyperbolic systems parametrized by a circle under assumptions involving the topological…
Recently, there is much interest in droplet condensation on soft or liquid/liquid-like substrates. Droplets can deform soft and liquid interfaces resulting in a wealth of phenomena not observed on hard, solid surfaces (e.g., increased…
Convection structures in binary fluid mixtures are investigated for positive Soret coupling in the driving regime where solutal and thermal contributions to the buoyancy forces compete. Bifurcation properties of stable and unstable…
We consider analytically and numerically head-on collision between two self-propelled drops. Each drop is driven by chemical reactions that produce or consume the concentration isotropically. The isotropic distribution of the concentration…
We study the phenomenon of the "walking droplet", by means of numerical fluid dynamics simulations using the Smoothed Particle Hydrodynamics numerical method. This phenomenon occurs when a millimetric drop is released on the surface of an…
We construct global curves of rotational traveling wave solutions to the $2D$ water wave equations on a compact domain. The real analytic interface is subject to surface tension, while gravitational effects are ignored. In contrast to the…
We discuss the dependence of set-valued dynamical systems on parameters. Under mild assumptions which are often satisfied for random dynamical systems with bounded noise and control systems, we establish the fact that topological…
We consider a thin droplet that spreads over a flat, horizontal and chemically heterogeneous surface. The droplet is subjected to changes in its volume though a prescribed, arbitrary spatiotemporal function, which varies slowly and vanishes…
Double Hopf bifurcation analysis can be used to reveal some complicated dynamical behavior in a dynamical system, such as the existence or coexistence of periodic orbits, quasi-periodic orbits, or even chaos. In this paper, an algorithm for…
Active droplets swim as a result of the nonlinear advective coupling of the distribution of chemical species they consume or release with the Marangoni flows created by their non-uniform surface distribution. Most existing models focus on…
Simulations show that when a phase-separated binary AB fluid is driven to flow past chemically patterned substrates in a microchannel, the fluid exhibits unique morphological instabilities. For the pattern studied, these instabilities give…