http://people.physik.hu-berlin.de/~lindner/PDF/physreport.pdf

Effects of noise in excitable systems

http://dadun.unav.edu/bitstream/10171/2018/1/2000.PhysRep.pdf

The control of chaos: theory and applications

46 structure types of binary and ternary intermetallic compounds have been derived from the well known, simple aristotype AlB 2 . Many compounds with the general compositions RX 2 , RT 2 , R7X, and R 2 TX 3 (R = alkaline earth, rare earth or actinoid metal: T = transition metal; X = main group element) belong to this family. The structural similarities between these compounds are manifested by an ordering of the transition metal atoms and main group element atoms on the boron positions of the AlB 2 type. Also an ordering of vacancies on the boron positions occurs in some compounds. Striking structural motifs of the RX 2 , RT 2 , RTX, and R 2 TX 3 compounds are planar or puckered six-membered rings consisting of X 6 , T 6 . T 3 X 3 , and T 2 X 4 separated by the respective R atoms The crystal chemical relationships between these compounds are discussed on the basis of a group-subgroup scheme in the concise and compact Barnighausen formalism with respect to the aristotype AlB 2 . Two different branches of AlB 2 related structures are discussed. In the first, the hexagonal/trigonal branch, six-membered rings carry at least a three-fold axis, while in the orthorhombic/ monoclinic branch the distortions are more pronounced. The pseudo-hexagons show significant tilting and a loss of hexagonal/trigonal symmetry. Significant variations of the chemical bonding occur for some structure types, and therefore they may only be considered to be isopointal rather than isotypic. These isopointal conversions are based on a gradual changeover from two- to three-dimensionally infinite polyanions. Besides the group theoretical group-subgroup scheme we also discuss chemical bonding in these AlB 2 related intermetallic compounds.

AlB2-related intermetallic compounds – a comprehensive view based on group-subgroup relations

We experimentally analyze the dynamics of a quantum dot semiconductor laser operating under optical injection. We observe the appearance of single- and double-pulse excitability at one boundary of the locking region. Theoretical considerations show that these pulses are related to a saddle-node bifurcation on a limit cycle as in the Adler equation. The double pulses are related to a period-doubling bifurcation and occur on the same homoclinic curve as the single pulses.

Excitability in a quantum dot semiconductor laser with optical injection.

The paper studies a novel excitability type where a large excitable response appears when a system’s parameter is varied gradually, or ramped, above some critical rate. This occurs even though there is a (unique) stable quiescent state for any fixed setting of the ramped parameter. We give a necessary and a sufficient condition for the existence of a critical ramping rate in a general class of slow–fast systems with folded slow (critical) manifold. Additionally, we derive an analytical condition for the critical rate by relating the excitability threshold to a canard trajectory through a folded saddle singularity. The general framework is used to explain a potential climate tipping point termed the ‘compost-bomb instability’—an explosive release of soil carbon from peatlands into the atmosphere occurs above some critical rate of global warming even though there is a unique asymptotically stable soil carbon equilibrium for any fixed atmospheric temperature.

/pdf/excitability-in-ramped-systems-the-compost-bomb-instability-1rg2epoaip.pdf

Excitability in ramped systems: the compost-bomb instability

Excitability and relaxation oscillations are shown to appear in the vicinity of subcritical or transcritical bifurcations with a different scenario from those previously introduced in biology, chemistry and liquid-crystal physics. Experimental observation of such a scenario has been done in a laser with intracavity saturable absorber.

https://fox.ino.it/home/arecchi/SezA/fis246.pdf

Excitability following an avalanche-collapse process

We propose a new type of excitability mechanism, based on an avalanche-collapse process. We show the differences and similarities between this and the already known excitability concepts for biological and mechanical systems. An experiment is also proposed with a laser containing a saturable absorber inside the cavity.

F. Plaza

Papers

Excitability following an avalanche-collapse process

Avalanche-collapse mechanism: a model for excitability