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We consider evolution of initial disturbances in spatially extended systems with autonomous rhythmic activity, such as the heart. We consider the case when the activity is stable with respect to very smooth (changing little across the…
Spatio-temporal dynamics of a deterministic three-level cellular automaton (TLCA) of Zykov-Mikhailov type (Sov. Phys. - Dokl., 1986, Vol.31, No.1, P.51) is studied numerically. Evolution of spatial structures is investigated both for the…
The Kuramoto model is a commonly used mathematical model for studying synchronized oscillations in biological systems, with its temporal synchronization properties well studied. However, the properties of spatial waves have received less…
We numerically study trajectories of spiral-wave-cores in excitable systems modulated proportionally to the integral of the activity on the straight line, several or dozens of equi-spaced measuring points on the straight line, the…
In a sub-excitable light-sensitive Belousov-Zhabotinsky chemical medium an asymmetric disturbance causes the formation of localized traveling wave-fragments. Under the right conditions these wave-fragment can conserve their shape and…
We investigate the dynamical behavior of rings around bodies whose shapes depart considerably from that of a sphere. To this end, we have developed a new self-gravitating discrete element N-body code, and employed a local simulation method…
Scroll waves are three-dimensional excitation patterns that rotate around a central filament curve; they occur in many physical, biological and chemical systems. We explicitly derive the equations of motion for scroll wave filaments in…
Perception-reaction delays have experimentally been found to cause a spontaneous circling of microswimmers around a targeted center. Here we investigate the many-body version of this experiment with Brownian-dynamics simulations of active…
Larval zebrafish exhibit a variety of complex undulatory swimming patterns. This repertoire is controlled by the 300 neurons projecting from brain into spinal cord. Understanding how descending control signals shape the output of spinal…
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 study the dynamics of a circadian oscillator model which was proposed by Tyson, Hong, Thron and Novak. This model indicates a molecular mechanism for the circadian rhythm in Drosophila. After giving a detailed study of the equilibria, we…
In bistable systems, the stability of front structures often influences the dynamics of extended patterns. We show how the combined effect of an instability to curvature modulations and proximity to a pitchfork front bifurcation leads to…
We observed the prototype blazar, BL Lacertae, extensively in optical and radio bands during an active phase in the period 2010--2013 when the source showed several prominent outbursts. We searched for possible correlations and time lags…
Numerical simulations of magnetosonic wave formation driven by an expanding cylindrical piston are performed to get better physical insight into the initiation and evolution of large-scale coronal waves. Several very basic initial…
Spin waves are the low-energy excitations of magnetically ordered materials. They are key elements in the stability analysis of the ordered phase and have a wealth of technological applications. Recently, we showed that spin waves of a…
GRS 1915+105 is a black hole X-ray binary exhibiting quasi-periodic $\rho$-class ("heartbeat") oscillations with periods of $\sim$50-100 s, thought to arise from radiation-pressure-driven instabilities in the inner accretion disk at…
We show that the breaking of the rotation symmetry of spiral waves in two-dimensional complex (period-doubled or chaotic) oscillatory media by synchronization defect lines (SDL) is accompanied by an intrinsic drift of the pattern. Single…
Several alternative methods for description of interaction between rotation and vibration are compared and contrasted using hyper-spherical coordinates for a triatomic molecule. These methods differ by the choice of z-axis and by the…
Gravitational waves are produced by orbiting massive binary objects, such as black holes and neutron stars, and propagate as ripples in the very fabric of spacetime. As the waves carry off orbital energy, the two bodies spiral into each…
Binary systems of rapidly spinning compact objects, such as black holes or neutron stars, are prime targets for gravitational wave astronomers. The dynamics of these systems can be very complicated due to spin-orbit and spin-spin couplings.…