Land-use type temporarily affects active pond community structure but not gene expression patterns.

Changes in land use and agricultural intensification threaten biodiversity and ecosystem functioning of small water bodies. We studied 67 kettle holes (KH) in an agricultural landscape in northeastern Germany using landscape-scale metatranscriptomics to understand the responses of active bacterial, archaeal and eukaryotic communities to land-use type. These KH are proxies of the millions of small standing water bodies of glacial origin spread across the northern hemisphere.

A probabilistic approach to dispersal in spatially explicit meta-populations.

Meta-population and -community models have extended our understanding regarding the influence of habitat distribution, local patch dynamics, and dispersal on species distribution patterns. Currently, theoretical insights on spatial distribution patterns are limited by the dominant use of deterministic approaches for modeling species dispersal. In this work, we introduce a probabilistic, network-based framework to describe species dispersal by considering inter-patch connections as network-determined probabilistic events.

Early warning signal for interior crises in excitable systems.

The ability to reliably predict critical transitions in dynamical systems is a long-standing goal of diverse scientific communities. Previous work focused on early warning signals related to local bifurcations (critical slowing down) and nonbifurcation-type transitions. We extend this toolbox and report on a characteristic scaling behavior (critical attractor growth) which is indicative of an impending global bifurcation, an interior crisis in excitable systems.

Linear Augmentation for Stabilizing Stationary Solutions: Potential Pitfalls and Their Application.

Linear augmentation has recently been shown to be effective in targeting desired stationary solutions, suppressing bistablity, in regulating the dynamics of drive response systems and in controlling the dynamics of hidden attractors. The simplicity of the procedure is the main highlight of this scheme but questions related to its general applicability still need to be addressed. Focusing on the issue of targeting stationary solutions, this work demonstrates instances where the scheme fails to stabilize the required solutions and leads to other complicated dynamical scenarios.

Route to extreme events in excitable systems.

Systems of FitzHugh-Nagumo units with different coupling topologies are capable of self-generating and -terminating strong deviations from their regular dynamics that can be regarded as extreme events due to their rareness and recurrent occurrence. Here we demonstrate the crucial role of an interior crisis in the emergence of extreme events. In parameter space we identify this interior crisis as the organizing center of the dynamics by employing concepts of mixed-mode oscillations and of leaking chaotic systems.

Extreme events in excitable systems and mechanisms of their generation.

We study deterministic systems, composed of excitable units of FitzHugh-Nagumo type, that are capable of self-generating and self-terminating strong deviations from their regular dynamics without the influence of noise or parameter change. These deviations are rare, short-lasting, and recurrent and can therefore be regarded as extreme events. Employing a range of methods we analyze dynamical properties of the systems, identifying features in the systems' dynamics that may qualify as precursors to extreme events.

Three-body interactions with time delay.

This work focuses on the dynamics of globally coupled phase oscillators with three-body interaction and time delay. Analytic estimates regarding the stability of the incoherent solution are presented. Expressions for the phase synchronization frequencies and their stability are also derived.

Frequency discontinuity and amplitude death with time-delay asymmetry.

We consider oscillators coupled with asymmetric time delays, namely, when the speed of information transfer is direction dependent. As the coupling parameter is varied, there is a regime of amplitude death within which there is a phase-flip transition. At this transition the frequency changes discontinuously, but unlike the equal delay case when the relative phase difference changes by π, here the phase difference changes by an arbitrary value that depends on the difference in delays.

Nature of the phase-flip transition in the synchronized approach to amplitude death.

We study the dynamics of time-delay coupled limit-cycle oscillators in the amplitude death regime. Through a detailed analysis of the Jacobian at the fixed point, we show that the phase-flip transition, namely, the abrupt change from in-phase synchronized dynamics to antiphase synchronized dynamics, is associated with an interchange of the imaginary parts of complex pairs of eigenvalues at an "avoided crossing" of Lyapunov exponents as a parameter is varied. An order parameter for the transition is constructed through the eigenvectors of the Jacobian.

Synchronization regimes in conjugate coupled chaotic oscillators.

Nonlinear oscillators that are mutually coupled via dissimilar (or conjugate) variables display distinct regimes of synchronous behavior. In identical chaotic oscillators diffusively coupled in this manner, complete synchronization occurs only by chaos suppression when the coupled subsystems drive each other into a regime of periodic dynamics. Furthermore, the coupling does not vanish but acts as an "internal" drive.

Universal occurrence of the phase-flip bifurcation in time-delay coupled systems.

Recently, the phase-flip bifurcation has been described as a fundamental transition in time-delay coupled, phase-synchronized nonlinear dynamical systems. The bifurcation is characterized by a change of the synchronized dynamics from being in-phase to antiphase, or vice versa; the phase-difference between the oscillators undergoes a jump of pi as a function of the coupling strength or the time delay. This phase-flip is accompanied by discontinuous changes in the frequency of the synchronized oscillators, and in the largest negative Lyapunov exponent or its derivative.

Amplitude death in the absence of time delays in identical coupled oscillators.

We study the dynamics of oscillators that are mutually coupled via dissimilar (or "conjugate") variables and find that this form of coupling leads to a regime of amplitude death. Analytic estimates are obtained for coupled Landau-Stuart oscillators, and this is supplemented by numerics for this system as well as for coupled Lorenz oscillators. Time delay does not appear to be necessary to cause amplitude death when conjugate variables are employed in coupling identical systems.