Generalized chronotaxic systems: time-dependent oscillatory dynamics stable under continuous perturbation

Chronotaxic systems represent deterministic nonautonomous oscillatory systems which are capable of resisting continuous external perturbations while having a complex time-dependent dynamics. Until their recent introduction in \emph{Phys. Rev. Lett.} \textbf{111}, 024101 (2013) chronotaxic systems had often been treated as stochastic, inappropriately, and the deterministic component had been ignored. While the previous work addressed the case of the decoupled amplitude and phase dynamics, in this paper we develop a generalized theory of chronotaxic systems where such decoupling is not required. The theory presented is based on the concept of a time-dependent point attractor or a driven steady state and on the contraction theory of dynamical systems. This simplifies the analysis of chronotaxic systems and makes possible the identification of chronotaxic systems with time-varying parameters. All types of chronotaxic dynamics are classified and their properties are discussed using the nonautonomous Poincar\'e oscillator as an example. We demonstrate that these types differ in their transient dynamics towards a driven steady state and according to their response to external perturbations. Various possible realizations of chronotaxic systems are discussed, including systems with temporal chronotaxicity and interacting chronotaxic systems.Comment: 9 pages, 8 figure

A unified framework for analysis of individual-based models in ecology and beyond

Individual-based models, 'IBMs', describe naturally the dynamics of interacting organisms or social or financial agents. They are considered too complex for mathematical analysis, but computer simulations of them cannot give the general insights required. Here, we resolve this problem with a general mathematical framework for IBMs containing interactions of an unlimited level of complexity, and derive equations that reliably approximate the effects of space and stochasticity. We provide software, specified in an accessible and intuitive graphical way, so any researcher can obtain analytical and simulation results for any particular IBM without algebraic manipulation. We illustrate the framework with examples from movement ecology, conservation biology, and evolutionary ecology. This framework will provide unprecedented insights into a hitherto intractable panoply of complex models across many scientific fields.Peer reviewe

Phases of the excitonic condensate in two-layer graphene

Two graphene monolayers that are oppositely charged and placed close to each other are considered. Taking into account valley and spin degeneracy of electrons we analyze the symmetry of the excitonic insulator states in such a system and build a phase diagram that takes into account the effect of the symmetry breaking due to the external in-plane magnetic field and the carrier density imbalance between the layers.Comment: 12 pages, 6 figures, 1 tabl

Estimating expansion of the range of oak processionary moth ( Thaumetopoea processionea ) in the UK from 2006 to 2019

Funder: Department for Environment, Food and Rural Affairs, UK GovernmentAbstract: The expansion of oak processionary moth (OPM) in South‐East England continues despite ongoing efforts to control the pest since its introduction in 2006. Using locations of OPM larval nests, supplied by the Forestry Commission and recorded as part of ongoing surveillance and control measures from 2006 onwards, we show that the expansion of the range of OPM in South‐East England up to 2019 was biphasic with a higher rate of expansion from 2015 onwards. The maximum rate of OPM range expansion in the United Kingdom from 2006 to 2014 was estimated as 1.66 km/year (95% CI = [1.22, 2.09]), whereas the 2015–2019 expansion rate was estimated as 6.17 km/year (95% CI = [5.49, 6.84]). This corresponds to an estimated species range distribution area of 7077 km2 in 2019. To explain the faster expansion of OPM range from 2015 onwards, we discuss potential reasons that include: natural capability of species of both short‐ and long‐distance dispersal; external factors such as environmental heterogeneity; a reduction of active control

Introduction to chronotaxic systems – systems far from thermodynamics equilibrium that adjust their clocks

The complex, fluctuating dynamics that abounds in nature is now easily monitored and analysed, applying either stochastic or deterministic methods. It has been demonstrated that complex systems far from thermodynamic equilibrium, especially living systems, often exhibit time-varying dynamics. To date they have been usually treated as stochastic. Here we focus on the non-autonomous properties of complex systems and propose a new class of dynamical systems. Namely, we assume that a basic dynamical unit which inherently possesses an internal source of energy, is continuously perturbed by the environment and maintains its stability by adjusting the rate of exchange of energy and matter with the environment. We provide a mathematical formalism for such systems, combining the recent theory of pullback attractors with the theory of self-sustained oscillators. We name the new class of systems as chronotaxic and, based on measured data, show that the heart possesses properties characteristic of chronotaxic systems. This means that its dynamics is largely deterministic, which opens new possibilities for diagnosis and prediction. We expect that many complex systems will be identified as chronotaxic and that their models will become much simpler and more realistic

Chronotaxic systems:a simple paradigm to treat time-dependent oscillatory dynamics stable under continuous perturbation

The treatment of non-autonomous systems is a challenging task, and one that arises in many branches of physics and science in general. The recently introduced notion of chronotaxic systems provides a new and promising approach to the problem. Chronotaxic dynamics is characterized by a time-dependent point attractor which exists in the timedependent contraction region. Chronotaxic systems are therefore capable of resisting continuous external perturbations while being characterised by complex time-dependent dynamics. The theory of chronotaxic systems, reviewed in this paper, together with corresponding inverse approach methods developed to tackle such systems, makes it possible to identify the underlying deterministic dynamics and to extract it. The resultant reduction of complexity may be useful in various scientific applications, especially in living systems

Chronotaxic systems with separable amplitude and phase dynamics

Until recently, deterministic non-autonomous oscillatory systems with stable amplitudes and time-varying frequencies were not recognised as such and have often been mistreated as stochastic. These systems, named chronotaxic, were introduced in \emph{Phys. Rev. Lett.} \textbf{111}, 024101 (2013). In contrast to conventional limit cycle models of self-sustained oscillators, these systems posses a time-dependent point attractor or steady state. This allows oscillations with time-varying frequencies to resist perturbations, a phenomenon which is ubiquitous in living systems. In this work a detailed theory of chronotaxic systems is presented, specifically in the case of separable amplitude and phase dynamics. The theory is extended by the introduction of chronotaxic amplitude dynamics. The wide applicability of chronotaxic systems to a range of fields from biological and condensed matter systems to robotics and control theory is discussed