Empirical models are central to effective conservation and population management, and should be predictive of real-world dynamics. Available modelling methods are diverse, but analysis usually focuses on long-term dynamics that are unable to describe the complicated short-term time series that can arise even from simple models following ecological disturbances or perturbations. Recent interest in such transient dynamics has led to diverse methodologies for their quantification in density-independent, time-invariant population projection matrix (PPM) models, but the fragmented nature of this literature has stifled the widespread analysis of transients. We review the literature on transient analyses of linear PPM models and synthesise a coherent framework. We promote the use of standardised indices, and categorise indices according to their focus on either convergence times or transient population density, and on either transient bounds or case-specific transient dynamics. We use a large database of empirical PPM models to explore relationships between indices of transient dynamics. This analysis promotes the use of population inertia as a simple, versatile and informative predictor of transient population density, but criticises the utility of established indices of convergence times. Our findings should guide further development of analyses of transient population dynamics using PPMs or other empirical modelling techniques.

Summary1. Population dynamics often defy predictions based on empirical models, and explanations for noisy dynamics have ranged from deterministic chaos to environmental stochasticity. Transient (short-term) dynamics following disturbance or perturbation have recently gained empirical attention from researchers as further possible effectors of complicated dynamics. 2. Previously published methods of transient analysis have tended to require knowledge of initial population structure. However, this has been overcome by the recent development of the parametric Kreiss bound (which describes how large a population must become before reaching its maximum possible transient amplification following a disturbance) and the extension of this and other transient indices to simultaneously describe both amplified and attenuated transient dynamics. 3. We apply the Kreiss bound and other transient indices to a data base of matrix models from 108 plant species, in an attempt to detect ecological and mathematical patterns in the transient dynamical properties of plant populations. 4. We describe how life history influences the transient dynamics of plant populations: species at opposite ends of the scale of ecological succession have the highest potential for transient amplification and attenuation, whereas species with intermediate life history complexity have the lowest potential. 5. We find ecological relationships between transients and asymptotic dynamics: faster-growing populations tend to have greater potential magnitudes of transient amplification and attenuation, which could suggest that short-and long-term dynamics are similarly influenced by demographic parameters or vital rates. 6. We describe a strong dependence of transient amplification and attenuation on matrix dimension: perhaps signifying a potentially worrying artefact of basic model parameterization. 7. Synthesis. Transient indices describe how big or how small plant populations can get, en route to long-term stable rates of increase or decline. The patterns we found in the potential for transient dynamics, across many species of plants, suggest a combination of ecological and modelling strategy influences. This better understanding of transients should guide the formulation of management and conservation strategies for all plant populations that suffer disturbances away from stable equilibria.

Abstract. Systems of globally coupled phase oscillators can have robust attractors that are heteroclinic networks. We investigate such a heteroclinic network between partially synchronized states where the phases cluster into three groups. For the coupling considered there exist 30 different three-cluster states in the case of five oscillators. We study the structure of the heteroclinic network and demonstrate that it is possible to navigate around the network by applying small impulsive inputs to the oscillator phases. This paper shows that such navigation may be done reliably even in the presence of noise and frequency detuning, as long as the input amplitude dominates the noise strength and the detuning magnitude, and the time between the applied pulses is in a suitable range. Furthermore, we show that, by exploiting the heteroclinic dynamics, frequency detuning can be encoded as a spatiotemporal code. By changing a coupling parameter we can stabilize the three-cluster states and replace the heteroclinic network by a network of excitable three-cluster states. The resulting "excitable network" has the same structure as the heteroclinic network and navigation around the excitable network is also possible by applying large impulsive inputs. We also discuss features that have implications for related models of neural activity.

Coronaviruses are a large family of viruses that cause different symptoms, from mild cold to severe respiratory distress, and they can be seen in different types of animals such as camels, cattle, cats and bats. Novel coronavirus called COVID-19 is a newly emerged virus that appeared in many countries of the world, but the actual source of the virus is not yet known. The outbreak has caused pandemic with 26,622,706 confirmed infections and 874,708 reported deaths worldwide till August 31, 2020, with 17,717,911 recovered cases. Currently, there exist no vaccines officially approved for the prevention or management of the disease, but alternative drugs meant for HIV, HBV, malaria and some other flus are used to treat this virus. In the present paper, a fractional-order epidemic model with two different operators called the classical Caputo operator and the Atangana–Baleanu–Caputo operator for the transmission of COVID-19 epidemic is proposed and analyzed. The reproduction number is obtained for the prediction and persistence of the disease. The dynamic behavior of the equilibria is studied by using fractional Routh–Hurwitz stability criterion and fractional La Salle invariant principle. Special attention is given to the global dynamics of the equilibria. Moreover, the fitting of parameters through least squares curve fitting technique is performed, and the average absolute relative error between COVID-19 actual cases and the model’s solution for the infectious class is tried to be reduced and the best fitted values of the relevant parameters are achieved. The numerical solution of the proposed COVID-19 fractional-order model under the Caputo operator is obtained by using generalized Adams–Bashforth–Moulton method, whereas for the Atangana–Baleanu–Caputo operator, we have used a new numerical scheme. Also, the treatment compartment is included in the population which determines the impact of alternative drugs applied for treating the infected individuals. Furthermore, numerical simulations of the model and their graphical presentations are performed to visualize the effectiveness of our theoretical results and to monitor the effect of arbitrary-order derivative.

Summary1. An important task in applied population ecology is to understand how changes to individual life-history parameters, such as survival, growth and fecundity, affect population dynamics. Parameter changes, or perturbations, may be caused by deliberate attempts to manage populations (e.g. in pest control, harvesting or conservation) or they may be side-effects of pollution, genetic modification and climate change. 2. For organisms with complicated life cycles, links between individual life histories and population dynamics are made using population projection matrix (PPM) modelling. 3. Changes to individual, or groups of, life-history transition rates within a PPM have a nonlinear impact on the resulting eigenvalues. Conventional sensitivity analysis calculates the derivative of the perturbation-eigenvalue curve to provide tangential linear extrapolation. Until now, only the simulation of perturbed PPMs has captured nonlinear perturbation effects. 4. Here we describe the transfer function of a matrix perturbation. The transfer function captures analytically the true relationship between perturbation magnitude and PPM eigenvalues. This analytical link extends easily to multi-transition and multiple perturbations, promotes an understanding of matrix properties, and provides a simple method to predict the perturbation required to achieve a desired population rate of increase. 5. We use the transfer function approach to analyse a PPM for the desert tortoise Gopherus agasizzii Cooper, in the context of conservation management decisions. 6. Synthesis and applications. The transfer function offers a novel and powerful framework for the analysis of population projection matrices (PPMs), giving precise predictive power and analytical understanding of population-level responses to life-history perturbations, for example in the design of conservation, pest control and population harvesting strategies, prediction of population effects of pollution in ecotoxicology, and in ecological risk assessment. A useful focus is to set a target for the desired rate of increase (or decline) of a population, and use the transfer function to determine how best to achieve this rate.

This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues.Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. b s t r a c tWe demonstrate that deterministic sea wave prediction (DSWP) combined with constrained optimal control can dramatically improve the efficiency of sea wave energy converters (WECs), while maintaining their safe operation. We focus on a point absorber WEC employing a hydraulic/electric power take-off system. Maximizing energy take-off while minimizing the risk of damage is formulated as an optimal control problem with a disturbance input (the sea elevation) and with both state and input constraints. This optimal control problem is non-convex, which prevents us from using quadratic programming algorithms for the optimal solution. We demonstrate that the optimum can be achieved by bangebang control. This paves the way to adopt a dynamic programming (DP) algorithm to resolve the on-line optimization problem efficiently. Simulation results show that this approach is very effective, yielding at least a two-fold increase in energy output as compared with control schemes which do not exploit DSWP. This level of improvement is possible even using relatively low precision DSWP over short time horizons. A key finding is that only about 1 second of prediction horizon is required, however, the technical difficulties involved in obtaining good estimates necessitate a DSWP system capable of prediction over tens of seconds.

Summary1. Ecological systems are prone to disturbances and perturbations. For stage-structured populations, communities and ecosystems, measurements of system magnitude in the short term will depend on how biased the stage structure is following a disturbance. 2. We promote the use of the Kreiss bound, a lower bound predictor of transient system magnitude that links transient amplification to system perturbations. The Kreiss bound is a simple and powerful alternative to other indices of transient dynamics, in particular reactivity and the amplification envelope. 3. We apply the Kreiss bound to a discrete-time model of an endangered species and a continuous-time rainforest model. 4. We promote the analysis of transient amplification relative to both initial conditions and asymptotic dynamics. 5. Transient amplification of ecological systems, following exogenous disturbances, has been implicated in the success of invasive species, persistence of extinction debts and species coexistence. 6. Synthesis and applications . The Kreiss bound allows simple assessment of transient amplification in ecological systems and the response of potential amplification to changes in system parameters. Hence it is an important tool for comparative analyses of ecological systems and should provide powerful predictions of optimal population management strategies.

One of the best-supported patterns in life history evolution is that organisms cope with environmental fluctuations by buffering their most important vital rates against them. This demographic buffering hypothesis is evidenced by a tendency for temporal variation in rates of survival and reproduction to correlate negatively with their contribution to fitness. Here, we show that widespread evidence for demographic buffering can be artefactual, resulting from natural relationships between the mean and variance of vital rates. Following statistical scaling, we find no significant tendency for plant life histories to be buffered demographically. Instead, some species are buffered, whereas others have labile life histories with higher temporal variation in their more important vital rates. We find phylogenetic signal in the strength and direction of variance-importance correlations, suggesting that clades of plants are prone to being either buffered or labile. Species with simple life histories are more likely to be demographically labile. Our results suggest important evolutionary nuances in how species deal with environmental fluctuations.