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. Like other landscapes in Europe, the study area has been used for intensive agriculture since the 1950s. In contrast to a parallel environmental DNA study that suggests the homogenization of biodiversity across KH, conceivably resulting from long-lasting intensive agriculture, land-use type affected the structure of the active KH communities during spring crop fertilization, but not a month later. This effect was more pronounced for eukaryotes than for bacteria. In contrast, gene expression patterns did not differ between months or across land-use types, suggesting a high degree of functional redundancy across the KH communities. Variability in gene expression was best explained by active bacterial and eukaryotic community structures, suggesting that these changes in functioning are primarily driven by interactions between organisms. Our results indicate that influences of the surrounding landscape result in temporary changes in the activity of different community members. Thus, even in KH where biodiversity has been homogenized, communities continue to respond to land management. This potential needs to be considered when developing sustainable management options for restoration purposes and for successful mitigation of further biodiversity loss in agricultural landscapes.

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. We highlight important differences between a deterministic approach and our dispersal formalism. Exemplified for a meta-population, our results indicate that the proposed scheme provides a realistic relationship between dispersal rate and extinction thresholds. Furthermore, it enables us to investigate the influence of patch density on meta-population persistence and provides insight on the effects of probabilistic dispersal events on species persistence. Importantly, our formalism makes it possible to capture the transient nature of inter-patch connections, and can thereby provide short term predictions on species distribution, which might be highly relevant for projections on how climate and land use changes influence species distribution patterns.

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. We demonstrate our early warning signal in a conceptual climate model as well as in a model of coupled neurons known to exhibit extreme events. We observed critical attractor growth prior to interior crises of chaotic as well as strange-nonchaotic attractors. These observations promise to extend the classes of transitions that can be predicted via early warning signals.

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. Examples from conservative as well as dissipative systems are presented in this regard and important applications in dissipative predator-prey systems are discussed, which include preventative measures to avoid potentially catastrophic dynamical transitions in these systems.

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. We find that extreme events occur in certain regions in parameter space, and we show the robustness of this phenomenon with respect to the system size.

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. We investigate these features and elucidate mechanisms that may be responsible for the generation of the 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. These theoretical results are supplemented with appropriate numerical computations. Numerical results regarding the fluctuations observed in the synchronization order parameter are then discussed. Some comparative results for phase synchronization in two-body, three-body, and mixed-coupled systems for different coupling combinations are also presented.

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. We consider asymmetric delays in coupled Landau-Stuart oscillators and Rössler oscillators. Analytical estimates of phase synchronization frequencies and phase differences are obtained by separating the evolution equations into phase and amplitude components. Eigenvalues and eigenvectors of the Jacobian matrix in the neighborhood of the transition also show an "avoided crossing," as has been observed in previous studies with symmetric 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. When the oscillators are mismatched, phase synchronization occurs, while in a master slave configuration, generalized synchrony results. These effects are demonstrated in a system of coupled chaotic Rossler oscillators.

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. Here we illustrate the phenomenology of the bifurcation for several classes of nonlinear oscillators, in the regimes of both periodic and chaotic dynamics. We present extensive numerical simulations and compute the oscillation frequencies and the Lyapunov spectra as a function of the coupling strength. In particular, our simulations provide clear evidence of the phase-flip bifurcation in excitable laser and Fitzhugh-Nagumo neuronal models, and in diffusively coupled predator-prey models with either limit cycle or chaotic dynamics. Our analysis demonstrates marked jumps of the time-delayed and instantaneous fluxes between the two interacting oscillators across the bifurcation; this has strong implications for the performance of the system as well as for practical applications. We further construct an electronic circuit consisting of two coupled Chua oscillators and provide the first formal experimental demonstration of the bifurcation. In totality, our study demonstrates that the phase-flip phenomenon is of broad relevance and importance for a wide range of physical and natural systems.

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. Coupled chaotic oscillators also show multistability prior to amplitude death, and the basins of the coexisting attractors appear to be riddled. This behavior is quantified: an appropriately defined uncertainty exponent in the coupled Lorenz system is shown to be zero.