Amplitude death in a pair of one-dimensional complex Ginzburg-Landau systems coupled by diffusive connections

Spatiotemporal patterns in coupled reaction-diffusion systems with nonidentical kinetics

Understanding of the effect of coupling interaction is at the heart of nonlinear science since some nonequilibrium systems are composed of different layers or units. In this paper, we demonstrate various spatio-temporal patterns in a nonlinearly coupled two-layer Turing system with nonidentical reaction kinetics. Both the type of Turing mode and coupling form play an important role in the pattern formation and pattern selection. Two kinds of Turing mode interactions, namely supercritical-subcritical and supercritical-supercritical Turing mode interaction, have been investigated. Stationary resonant superlattice patterns arise spontaneously in both cases, while dynamic patterns can also be formed in the latter case. The destabilization of spike solutions induced by spatial heterogeneity may be responsible for these dynamic patterns. In contrast to linear coupling, the nonlinear coupling not only increases the complexity of spatio-temporal patterns, but also reduces the requirements of spatial resonance conditions. The simulation results are in good agreement with the experimental observations in dielectric barrier discharge systems.

Effects of frequency mismatch on amplitude death in delay-coupled oscillators

The present paper analytically reveals the effects of frequency mismatch on the stability of an equilibrium point within a pair of Stuart-Landau oscillators coupled by a delay connection. By analyzing the roots of the characteristic function governing the stability, we find that there exist four types of boundary curves of stability in a coupling parameters space. These four types depend only on the frequency mismatch. The analytical results allow us to design coupling parameters and frequency mismatch such that the equilibrium point is locally stable. We show that, if we choose appropriate frequency mismatches and delay times, then it is possible to induce amplitude death with strong stability, even by weak coupling. In addition, we show that parts of these analytical results are valid for oscillator networks with complete bipartite topologies.

Predicting amplitude death with machine learning

In nonlinear dynamics, a parameter drift can lead to a sudden and complete cessation of the oscillations of the state variables-the phenomenon of amplitude death. The underlying bifurcation is one at which the system settles into a steady state from chaotic or regular oscillations. As the normal functioning of many physical, biological, and physiological systems hinges on oscillations, amplitude death is undesired. To predict amplitude death in advance of its occurrence based solely on oscillatory time series collected while the system still functions normally is a challenge problem. We exploit machine learning to meet this challenge. In particular, we develop the scheme of "parameter-aware" reservoir computing, where training is conducted for a small number of bifurcation parameter values in the oscillatory regime to enable prediction upon a parameter drift into the regime of amplitude death. We demonstrate successful prediction of amplitude death for three prototypical dynamical systems in which the transition to death is preceded by either chaotic or regular oscillations. Because of the completely data-driven nature of the prediction framework, potential applications to real-world systems can be anticipated.

Amplitude suppression of oscillators with delay connections and slow switching topology

The present paper shows that the amplitudes of oscillators in delay-coupled oscillator networks can be suppressed by switching the network topology at a rate much lower than the oscillator frequencies. The mechanism of suppression was clarified numerically, and a procedure for determining the connection parameters to induce suppression is presented. The analytical and numerical results were obtained with Stuart-Landau oscillators and were experimentally validated using double-scroll chaotic circuits.

Overexpression of striatal D2 receptors reduces motivation thereby decreasing food anticipatory activity

Dopamine has been implicated in circadian timing underlying the food entrainable oscillator (FEO) circuitry and overexpression of the dopamine D2 receptor (D2R) in the striatum has been reported to reduce motivation to obtain food rewards in operant tasks. In the present study, we explored both of these mechanisms by examining food anticipatory activity (FAA) in dopamine D2 receptor-overexpressing (D2R-OE) mice under various durations of food availability. First, we noted that at baseline, there were no differences between D2R-OE mice and their littermates in activity level, food intake, and body weight or in circadian activity. Under conditions of very restricted food availability (4 or 6 hr), both genotypes displayed FAA. In contrast, under 8-hr food availability, control mice showed FAA, but D2R-OE mice did not. Normalization of D2R by administration of doxycycline, a tetracycline analogue, rescued FAA under 8-hr restricted food. We next tested for circadian regulation of FAA. When given ad libitum access to food, neither D2R-OE nor controls were active during the daytime. However, after an interval of food restriction, all mice showed elevated locomotor activity at the time of previous food availability in the day, indicating circadian timing of anticipatory activity. In summary, motivation is reduced in D2R-OE mice but circadian timing behavior is not affected. We conclude that an increase in striatal D2R reduces FAA by modulating motivation and not by acting on a clock mechanism.

Stabilization of a spatially uniform steady state in two systems exhibiting Turing patterns

This paper deals with the stabilization of a spatially uniform steady state in two coupled one-dimensional reaction-diffusion systems with Turing instability. This stabilization corresponds to amplitude death that occurs in a coupled system with Turing instability. Stability analysis of the steady state shows that stabilization does not occur if the two reaction-diffusion systems are identical. We derive a sufficient condition for the steady state to be stable for any length of system and any boundary conditions. Our analytical results are supported with numerical examples.