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It is proposed that the spatial (and temporal) patterns spontaneously appearing in dissipative systems maximize the energy flow through the pattern forming interface. In other words - the patterns maximize the entropy growth rate in an…
Self-oscillations are the result of an efficient mechanism generating periodic motion from a constant power source. In quantum devices, these oscillations may arise due to the interaction between single electron dynamics and mechanical…
We consider the model of fiber-laser cavities near the zero-dispersion point, based on the complex Ginzburg-Landau equation with the cubic-quintic nonlinearity, including the third-order dispersion (TOD) term. It is well known that this…
Diffusion within porous media, such as biological tissues, exhibits departures from conventional Fick's laws, which could result in space-fractional diffusion. The paper considers a reaction-diffusion system with two spatial compartments --…
The passively Q-switched, self-pulsing all-solid-state laser is a device of widespread use in many applications. Depending on the condition of saturation, which is easy to adjust, different dynamical phenomena are observed: continuous wave…
Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of…
In this Chapter we investigate with the methods of signal detection the response of a Josephson junction to a perturbation to decide if the perturbation contains a coherent oscillation embedded in the background noise. When a Josephson…
The diffusion of an artificial active particle in a two-dimensional periodic pattern of stationary convection cells is investigated by means of extensive numerical simulations. In the limit of large P\'eclet numbers, i.e., for…
The spontaneous generation of electrical activity underpins a number of essential physiological processes, and is observed even in tissues where specialized pacemaker cells have not been identified. The emergence of periodic oscillations in…
We study the dynamics of scroll vortices in excitable reaction-diffusion systems analytically and numerically. We demonstrate that intrinsic three-dimensional instability of a straight scroll leads to the formation of helicoidal structures.…
Pattern formation from homogeneity is well-studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is nontrivial to separate observed spatial patterning due to inherent spatial heterogeneity from…
The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental…
Oscillons are extremely long-lived, spatially-localized field configurations in real-valued scalar field theories that slowly lose energy via radiation of scalar waves. Before their eventual demise, oscillons can pass through (one or more)…
Highly collimated supersonic jets and less collimated outflows are observed to emerge from a wide variety of astrophysical objects. They are seen in young stellar objects (YSOs), proto-planetary nebulae, compact objects (like galactic black…
Many natural or human-made systems encompassing local reactions and diffusion processes exhibit spatially distributed patterns of some relevant dynamical variable. These interactions, through self-organization and critical phenomena, give…
Diffusion occurs in numerous physical systems throughout nature, drawing its generality from the universality of the central limit theorem. Around a century ago it was realized that an extension to this type of dynamics can be obtained in…
It has been recently suggested that oscillons produced in the early universe from certain asymmetric potentials continue to emit gravitational waves for a number of $e$-folds of expansion after their formation, leading to potentially…
Oscillation of macroscopic variables is discovered in a metastable state in the Hamiltonian dynamical system of mean field XY model, the duration of which is divergent with the system size. This long-lasting periodic or quasiperiodic…
Droplets moving in a microfluidic loop device exhibit both periodic and chaotic behaviors based on the inlet droplet spacing. We propose that the periodic behavior is an outcome of a dispersed phase conservation principle. This conservation…
We consider a dynamical system consisting of subsystems indexed by a lattice. Each subsystem has one conserved degree of freedom ("energy") the rest being uniformly hyperbolic. The subsystems are weakly coupled together so that the sum of…