Fractalization of Torus Revisited as a Strange Nonchaotic Attractor

Fractalization of torus and its transition to chaos in a quasi-periodically forced logistic map is re-investigated in relation with a strange nonchaotic attractor, with the aid of functional equation for the invariant curve. Existence of fractal torus in an interval in parameter space is confirmed by the length and the number of extrema of the torus attractor, as well as the Fourier mode analysis. Mechanisms of the onset of fractal torus and the transition to chaos are studied in connection with the intermittency.Comment: Latex file ( figures will be sent electronically upon request):submitted to Phys.Rev. E (1996

Resonance phenomena of a solitonlike extended object in a bistable potential

We investigate the dynamics of a soliton that behaves as an extended particle. The soliton motion in an effective bistable potential can be chaotic in a similar way as the Duffing oscillator. We generalize the concept of geometrical resonance to spatiotemporal systems and apply it to design a nonfeedback mechanism of chaos control using localized perturbations.We show the existence of solitonic stochastic resonance.Comment: 3 postscript figure

Effect of noise on coupled chaotic systems

Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by identical noise, show synchronization phenomena where chaotic trajectories exponentially converge towards a single noisy trajectory, independent of the initial conditions. In a random neural network, with infinite range coupling, chaos is suppressed due to noise and the system evolves towards a fixed point. Spatiotemporal stochastic resonance phenomenon has been observed in a square array of coupled threshold devices where a temporal characteristic of the system resonates at a given noise strength. In a chaotically evolving coupled map lattice with logistic map as local dynamics and driven by identical noise at each site, we report that the number of structures (a structure is a group of neighbouring lattice sites for whom values of the variable follow certain predefined pattern) follow a power-law decay with the length of the structure. An interesting phenomenon, which we call stochastic coherence, is also reported in which the abundance and lifetimes of these structures show characteristic peaks at some intermediate noise strength.Comment: 21 page LaTeX file for text, 5 Postscript files for figure

The Healthy Primary School of the Future:study protocol of a quasi-experimental study

Background: Unhealthy lifestyles in early childhood are a major global health challenge. These lifestyles often persist from generation to generation and contribute to a vicious cycle of health-related and social problems. This design article presents a study evaluating the effects of two novel healthy school interventions. The main outcome measure will be changes in children's body mass index (BMI). In addition, lifestyle behaviours, academic achievement, child well-being, socio-economic differences, and societal costs will be examined. Methods: In close collaboration with various stakeholders, a quasi-experimental study was developed, for which children of four intervention schools (n = 1200) in the southern part of the Netherlands are compared with children of four control schools (n = 1200) in the same region. The interventions started in November 2015. In two of the four intervention schools, a whole-school approach named 'The Healthy Primary School of the Future', is implemented with the aim of improving physical activity and dietary behaviour. For this intervention, pupils are offered an extended curriculum, including a healthy lunch, more physical exercises, and social and educational activities, next to the regular school curriculum. In the two other intervention schools, a physical-activity school approach called 'The Physical Activity School', is implemented, which is essentially similar to the other intervention, except that no lunch is provided. The interventions proceed during a period of 4 years. Apart from the effectiveness of both interventions, the process, the cost-effectiveness, and the expected legal implications are studied. Data collection is conducted within the school system. The baseline measurements started in September 2015 and yearly follow-up measurements are taking place until 2019. Discussion: A whole-school approach is a new concept in the Netherlands. Due to its innovative, multifaceted nature and sound scientific foundation, these integrated programmes have the potential to form a template for primary schools worldwide. The effects of this approach may extend further than the outcomes associated with well-being and academic achievement, potentially impacting legal and cultural aspects in our society. Trial registration: The study protocol was registered in the database ClinicalTrials.gov on 14-06-2016 with the reference number NCT02800616

Memory in Microbes: Quantifying History-Dependent Behavior in a Bacterium

Memory is usually associated with higher organisms rather than bacteria. However, evidence is mounting that many regulatory networks within bacteria are capable of complex dynamics and multi-stable behaviors that have been linked to memory in other systems. Moreover, it is recognized that bacteria that have experienced different environmental histories may respond differently to current conditions. These “memory” effects may be more than incidental to the regulatory mechanisms controlling acclimation or to the status of the metabolic stores. Rather, they may be regulated by the cell and confer fitness to the organism in the evolutionary game it participates in. Here, we propose that history-dependent behavior is a potentially important manifestation of memory, worth classifying and quantifying. To this end, we develop an information-theory based conceptual framework for measuring both the persistence of memory in microbes and the amount of information about the past encoded in history-dependent dynamics. This method produces a phenomenological measure of cellular memory without regard to the specific cellular mechanisms encoding it. We then apply this framework to a strain of Bacillus subtilis engineered to report on commitment to sporulation and degradative enzyme (AprE) synthesis and estimate the capacity of these systems and growth dynamics to ‘remember’ 10 distinct cell histories prior to application of a common stressor. The analysis suggests that B. subtilis remembers, both in short and long term, aspects of its cell history, and that this memory is distributed differently among the observables. While this study does not examine the mechanistic bases for memory, it presents a framework for quantifying memory in cellular behaviors and is thus a starting point for studying new questions about cellular regulation and evolutionary strategy

Differentiation in a globally coupled circle map with growth and death

A key characteristic of biological systems is the continuous life cycle where cells are born, grow and die. From a dynamical point of view the events of cell division and cell death are of paramount importance and constitute a radical departure from systems with a fixed size. In this paper, a globally coupled circle map where elements can dynamically be added and removed is investigated for the conditions under which differentiation of roles can occur. In the presence of an external source, it is found that populations of very long-living cells are sustained by short-living cells. In the case without an external source, it is found that at higher nonlinearities of the local map, large populations cannot be sustained with a previously employed division strategy but that a different and conceptually equally natural division strategy allows for differentiation of roles. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005