The effect of time delay in plant-pathogen interactions with host demography

Background: There is a need for valid and comprehensive measures of parental influence on children's energy balance-related behaviours (EBRB). Such measures should be based on a theoretical framework, acknowledging the dynamic and complex nature of interactions occurring within a family. The aim of the Family & Dietary habits (F&D) project was to develop a conceptual framework identifying important and changeable family processes influencing dietary behaviours of 13-15 year olds. A second aim was to develop valid and reliable questionnaires for adolescents and their parents (both mothers and fathers) measuring these processes. Methods: A stepwise approach was used; (1) preparation of scope and structure, (2) development of the F&D questionnaires, (3) the conducting of pilot studies and (4) the conducting of validation studies (assessing internal reliability, test-retest reliability and confirmatory factor analysis) using data from a cross-sectional study. Results: The conceptual framework includes psychosocial concepts such as family functioning, cohesion, conflicts, communication, work-family stress, parental practices and parental style. The physical characteristics of the home environment include accessibility and availability of different food items, while family meals are the sociocultural setting included. Individual characteristics measured are dietary intake (vegetables and sugar-sweetened beverages) and adolescents' impulsivity. The F&D questionnaires developed were tested in a test-retest (54 adolescents and 44 of their parents) and in a cross-sectional survey including 440 adolescents (13-15 year olds), 242 mothers and 155 fathers. The samples appear to be relatively representative for Norwegian adolescents and parents. For adolescents, mothers and fathers, the test-retest reliability of the dietary intake, frequencies of (family) meals, work-family stress and communication variables was satisfactory (ICC: 0.53-0.99). Barratt Impulsiveness Scale-Brief (BIS-Brief) was included, assessing adolescent's impulsivity. The internal reliability (Cronbach's alphas: 0.77/0.82) and test-retest reliability values (ICC: 0.74/0.77) of BIS-Brief were good. Conclusions: The conceptual framework developed may be a useful tool in guiding measurement and assessment of the home food environment and family processes related to adolescents' dietary habits, in particular and for EBRBs more generally. The results support the use of the F&D questionnaires as psychometrically sound tools to assess family characteristics and adolescent's impulsivity

On the interaction of rate-induced and bifurcation-induced tipping in ecosystems

We analyse nonlinear tipping phenomena in a bi-stable ecosystem model, defined as sudden and unexpected transitions from the herbivore-dominating equilibrium to the plant-only equilibrium, which are triggered by environmental changes represented by time-varying parameters [Scheffer et al. {\em Ecosystems} 11 2008]. We obtain simple criteria for tipping in terms of properties of the autonomous system with fixed in time parameters. Specifically, we use classical bifurcation analysis to identify a codimension-three degenerate Bogdanov-Takens bifurcation: the organising centre for bifurcation-induced tipping (B-tipping) and the source of a dangerous subcritical Hopf bifurcation. We introduce basin instability analysis to identify parameter paths along which rate-induced tipping (R-tipping) is guaranteed to occur without crossing any bifurcation. We then produce tipping diagrams for the non-autonomous system with time-varying parameters in the plane of the magnitude and rate of a parameter shift to reveal tipping-tracking transitions due to maximal-canard solutions that, perhaps surprisingly, follow unstable states for infinite time. We also uncover non-trivial dynamics arising from the interaction between B-tipping and R-tipping. Given a monotone parameter shift that causes tipping, we ask if tipping can be prevented upon a parameter trend reversal. The ensuing analysis of non-monotone parameter shifts reveals an intriguing tipping diagram with a single critical level and multiple critical rates, indicating that the system switches from tipping to tracking and back to tipping again as the rate of the parameter shift increases. In the diagram, we identify points of no return where tipping cannot be prevented by the parameter trend reversal and points of return tipping where tipping is inadvertently induced by the parameter trend reversal. The results give new insight into the sensitivity of ecosystems to the magnitudes and rates of environmental change. A comparison of the ecosystem model with modified saddle-node and subcritical Hopf normal forms shows that the tipping diagram is characteristic of a non-monotone passage through a basin instability boundary and a generic dangerous bifurcation in nonlinear systems in general

Ion Channel Density Regulates Switches between Regular and Fast Spiking in Soma but Not in Axons

The threshold firing frequency of a neuron is a characterizing feature of its dynamical behaviour, in turn determining its role in the oscillatory activity of the brain. Two main types of dynamics have been identified in brain neurons. Type 1 dynamics (regular spiking) shows a continuous relationship between frequency and stimulation current (f-Istim) and, thus, an arbitrarily low frequency at threshold current; Type 2 (fast spiking) shows a discontinuous f-Istim relationship and a minimum threshold frequency. In a previous study of a hippocampal neuron model, we demonstrated that its dynamics could be of both Type 1 and Type 2, depending on ion channel density. In the present study we analyse the effect of varying channel density on threshold firing frequency on two well-studied axon membranes, namely the frog myelinated axon and the squid giant axon. Moreover, we analyse the hippocampal neuron model in more detail. The models are all based on voltage-clamp studies, thus comprising experimentally measurable parameters. The choice of analysing effects of channel density modifications is due to their physiological and pharmacological relevance. We show, using bifurcation analysis, that both axon models display exclusively Type 2 dynamics, independently of ion channel density. Nevertheless, both models have a region in the channel-density plane characterized by an N-shaped steady-state current-voltage relationship (a prerequisite for Type 1 dynamics and associated with this type of dynamics in the hippocampal model). In summary, our results suggest that the hippocampal soma and the two axon membranes represent two distinct kinds of membranes; membranes with a channel-density dependent switching between Type 1 and 2 dynamics, and membranes with a channel-density independent dynamics. The difference between the two membrane types suggests functional differences, compatible with a more flexible role of the soma membrane than that of the axon membrane

Bifurcation analysis of a population model and the resulting SIS epidemic model with delay

AbstractThis paper deals with the model for matured population growth proposed in Cooke et al. [Interaction of matiration delay and nonlinear birth in population and epidemic models, J. Math. Biol. 39 (1999) 332–352] and the resulting SIS epidemic model. The dynamics of these two models are still largely undetermined, and in this paper, we perform some bifurcation analysis to the models. By applying the global bifurcation theory for functional differential equations, we are able to show that the population model allows multiple periodic solutions. For the SIS model, we obtain some local bifurcation results and derive formulas for determining the bifurcation direction and the stability of the bifurcated periodic solution

Stochastic analysis of nonlinear dynamics and feedback control for gene regulatory networks with applications to synthetic biology

The focus of the thesis is the investigation of the generalized repressilator model (repressing genes ordered in a ring structure). Using nonlinear bifurcation analysis stable and quasi-stable periodic orbits in this genetic network are characterized and a design for a switchable and controllable genetic oscillator is proposed. The oscillator operates around a quasi-stable periodic orbit using the classical engineering idea of read-out based control. Previous genetic oscillators have been designed around stable periodic orbits, however we explore the possibility of quasi-stable periodic orbit expecting better controllability. The ring topology of the generalized repressilator model has spatio-temporal symmetries that can be understood as propagating perturbations in discrete lattices. Network topology is a universal cross-discipline transferable concept and based on it analytical conditions for the emergence of stable and quasi-stable periodic orbits are derived. Also the length and distribution of quasi-stable oscillations are obtained. The findings suggest that long-lived transient dynamics due to feedback loops can dominate gene network dynamics. Taking the stochastic nature of gene expression into account a master equation for the generalized repressilator is derived. The stochasticity is shown to influence the onset of bifurcations and quality of oscillations. Internal noise is shown to have an overall stabilizing effect on the oscillating transients emerging from the quasi-stable periodic orbits. The insights from the read-out based control scheme for the genetic oscillator lead us to the idea to implement an algorithmic controller, which would direct any genetic circuit to a desired state. The algorithm operates model-free, i.e. in principle it is applicable to any genetic network and the input information is a data matrix of measured time series from the network dynamics. The application areas for readout-based control in genetic networks range from classical tissue engineering to stem cells specification, whenever a quantitatively and temporarily targeted intervention is required