Sulfonylurea Receptor Pharmacology Alters the Performance of Two Central Pattern Generating Circuits in Cancer borealis.

Neuronal activity and energy supply must maintain a fine balance for neuronal fitness. Various channels of communication between the two could impact network output in different ways. Sulfonylurea receptors (SURs) are a modification of ATP-binding cassette proteins that confer ATP-dependent gating on their associated ion channels.

Sulfonylurea receptor coupled conductances alter the performace of two central pattern generating circuits in .

Neuronal activity and energy supply must maintain a fine balance for neuronal fitness. Various channels of communication between the two could impact network output in different ways. Sulfonylurea receptors (SURs) are a modification of ATP-binding cassette proteins (ABCs) that confer ATP-dependent gating on their associated ion channels.

Strong symmetry breaking rhythms created by folded nodes in a pair of symmetrically coupled, identical Koper oscillators.

The Koper model is a prototype system with two slow variables and one fast variable that possesses small-amplitude oscillations (SAOs), large-amplitude oscillations (LAOs), and mixed-mode oscillations (MMOs). In this article, we study a pair of identical Koper oscillators that are symmetrically coupled. Strong symmetry breaking rhythms are presented of the types SAO-LAO, SAO-MMO, LAO-MMO, and MMO-MMO, in which the oscillators simultaneously exhibit rhythms of different types.

Symmetry-breaking rhythms in coupled, identical fast-slow oscillators.

Symmetry-breaking in coupled, identical, fast-slow systems produces a rich, dramatic variety of dynamical behavior-such as amplitudes and frequencies differing by an order of magnitude or more and qualitatively different rhythms between oscillators, corresponding to different functional states. We present a novel method for analyzing these systems. It identifies the key geometric structures responsible for this new symmetry-breaking, and it shows that many different types of symmetry-breaking rhythms arise robustly.

Period-doubling route to mixed-mode chaos.

Mixed-mode oscillations (MMOs) are a complex dynamical behavior in which each cycle of oscillation consists of one or more large amplitude spikes followed by one or more small amplitude peaks. MMOs typically undergo period-adding bifurcations under parameter variation. We demonstrate here, in a set of three identical, linearly coupled van der Pol oscillators, a scenario in which MMOs exhibit a period-doubling sequence to chaos that preserves the MMO structure, as well as period-adding bifurcations.

Post-canard symmetry breaking and other exotic dynamic behaviors in identical coupled chemical oscillators.

We analyze a model of two identical chemical oscillators coupled through diffusion of the slow variable. As a parameter is varied, a single oscillator undergoes a canard explosion-a transition from small amplitude, nearly harmonic oscillations to large-amplitude, relaxation oscillations over a very small parameter interval. In the coupled system, if the two oscillators have the same initial conditions, then the oscillators remain synchronized and exhibit the same canard behavior observed for the single oscillator.

The smallest chimera: Periodicity and chaos in a pair of coupled chemical oscillators.

Symmetrically coupled identical oscillators were once believed to support only totally synchronous or totally asynchronous states. More recently, chimera states, in which a subset of oscillators behaves coherently while the other subset exhibits disorder, have been found in large arrays of oscillators, coupled either locally or globally. We demonstrate for the first time the existence of a chimera state with only two diffusively coupled identical oscillators, one behaving nearly periodically (coherently) and the other chaotically (incoherently).