Stationary spatially localized structures, sometimes called dissipative solitons, arise in many
interesting and important applications, including buckling of slender structures under …

Coherent structures emerge from the dynamics of many kinds of dissipative, externally
driven, nonlinear systems, and continue to provoke new questions that challenge our …

The Turing reaction-diffusion model explains how identical cells can self-organize to form
spatial patterns. It has been suggested that extracellular signaling molecules with different …

We present a benchmark study of autonomous, chemical agents exhibiting associative
learning of an environmental feature. Associative learning systems have been widely …

Steady states of localized activity appear naturally in uniformly driven, dissipative systems as
a result of subcritical instabilities. In the usual setting of an infinite domain, branches of such …

The understanding of self-organized patterns in spatially extended nonlinear dissipative
systems is one of the most challenging subjects in modern natural sciences. Such patterns …

We explain the notion of dissipative solitons within a historical perspective. We show that the
ideas of the theory of dissipative solitons emerge from several fields, including classical …

Identifying approaching bifurcations and regime transitions from observations is an
important challenge in time series analysis with practical applications in many fields of …

We study the linear stability properties of spatially localized single-and multi-peak states
generated in a subcritical Turing bifurcation in the Meinhardt model of branching. In one …

We study the reaction kinetics of chemical processes occurring in the ultracold regime and
systematically investigate their dynamics. Quantum entanglement is found to play a key role …