James Rankin

Characterizing Dynamic Interactions between Ultradian Glucocorticoid Rhythmicity and Acute Stress Using the Phase Response Curve

The hypothalamic-pituitary-adrenal (HPA) axis is a dynamic oscillatory hormone signalling system that regulates the pulsatile secretion of glucocorticoids from the adrenal glands. In addition to regulation of basal levels of glucocorticoids, the HPA axis provides a rapid hormonal response to stress that is vitally important for homeostasis. Recently it has become clear that glucocorticoid pulses encode an important biological signal that regulates receptor signalling both in the central nervous system and in peripheral tissues. It is therefore important to understand how stressful stimuli disrupt the pulsatile dynamics of this system. Using a computational model that incorporates the crucial feed-forward and feedback components of the axis, we provide novel insight into experimental observations that the size of the stress-induced hormonal response is critically dependent on the timing of the stress. Further, we employ the theory of Phase Response Curves to show that an acute stressor acts as a phase-resetting mechanism for the ultradian rhythm of glucocorticoid secretion. Using our model, we demonstrate that the magnitude of an acute stress is a critical factor in determining whether the system resets via a Type 1 or Type 0 mechanism. By fitting our model to our in vivo stress-response data, we show that the glucocorticoid response to an acute noise stress in rats is governed by a Type 0 phase-resetting curve. Our results provide additional evidence for the concept of a deterministic sub-hypothalamic oscillator regulating the ultradian glucocorticoid rhythm, which constitutes a highly responsive peripheral hormone system that interacts dynamically with hypothalamic inputs to regulate the overall hormonal response to stress.

Bifurcation and Stability Analysis of Aircraft Turning on the Ground

During ground maneuvers a loss of lateral stability due to the saturation of the main landing gear tires can cause the aircraft to enter a skid or a spin. The lateral stability is governed not only by aspects of the gear design, such as its geometry and tire characteristics, but also by operational parameters: for example, the weather and taxiway condition. In this paper, we develop an improved understanding and new presentation of the dynamics of an aircraft maneuvering on the ground, ultimately aimed at optimization and automation of ground operations. To investigate turning maneuvers, we apply techniques from dynamic systems theory to a modified version of a nonlinear computer model of an A320 passenger aircraft developed by the Landing Gear Group at Airbus in the United Kingdom. Specifically, we present a bifurcation analysis of the underlying solution structure that governs the dynamics of turning maneuvers with dependence on the steering angle and thrust level. Furthermore, a detailed study of the behavior when lateral stability is lost focuses on how the tire saturation at different wheel sets leads to qualitatively different types of overall behavior. The presented bifurcation diagrams identify parameter regions for which undesirable behavior is avoidable, and thus they form a foundation for defining the safe operating limits during turning maneuvers.

Continuation of Localized Coherent Structures in Nonlocal Neural Field Equations

We study localized activity patterns in neural field equations posed on the Euclidean plane; such models are commonly used to describe the coarse-grained activity of large ensembles of cortical neurons in a spatially continuous way. We employ matrix-free Newton--Krylov solvers and perform numerical continuation of localized patterns directly on the integral form of the equation. This opens up the possibility of studying systems whose synaptic kernel does not lead to an equivalent PDE formulation. We present a numerical bifurcation study of localized states and show that the proposed models support patterns of activity with varying spatial extent through the mechanism of homoclinic snaking. The regular organization of these patterns is due to spatial interactions at a specific scale associated with the separation of excitation peaks in the chosen connectivity function. The results presented form a basis for the general study of localized cortical activity with inputs and, more specifically, for the investi...

Operational Parameter Study of Aircraft Dynamics on the Ground

The dynamics of passenger aircraft on the ground are influenced by the nonlinear characteristics of several components, including geometric nonlinearities, aerodynamics, and interactions at the tire-ground interface. We present a fully parameterized mathematical model of a typical passenger aircraft that includes all relevant nonlinear effects. The full equations of motion are derived from first principles in terms of forces and moments acting on a rigid airframe, and they include implementations of the local models of individual components. The overall model has been developed from and validated against an existing industry-tested SIMMECHANICS model. The key advantage of the mathematical model is that it allows for comprehensive studies of solutions and their stability with methods from dynamical systems theory, particularly, the powerful tool of numerical continuation. As a concrete example, we present a bifurcation study of how fixed-radius turning solutions depend on the aircrafts steering angle and center of gravity position. These results are represented in a compact form as surfaces of solutions, on which we identify regions of stable turning and regions of laterally unstable solutions. The boundaries between these regions are computed directly, and they allow us to determine ranges of parameter values for safe operation. The robustness of these results under the variation in additional parameters, specifically, the engine thrust and aircraft mass, are investigated. Qualitative changes in the structure of the solutions are identified and explained in detail. Overall our results give a complete description of the possible turning dynamics of the aircraft in dependence on four parameters of operational relevance.

Nonlinear Analysis of Lateral Loading During Taxiway Turns

determined by the maximal lateral loading conditions identified in published studies of instrumented in-service passenger aircraft. The performance of the turn can be assessed over the entire operational range in terms of the actual loads experienced at individual landing gears. Recent studies by the Federal Aviation Administration of instrumented aircraft have been limited to investigating the lateral loads experienced at the aircraft’s center-ofgravity position. The results presented here show that this information is insufficient to predict the actual loads experienced by individual landing gears, especially for the nose gear, which is found to experience considerably higher lateral loads than predicted by the corresponding loads at center of gravity. These findings are shown to be robust with respect to changes in the aircraft’s mass and the criterion used to define the limits of the operating regions.

Bifurcation study of a neural field competition model with an application to perceptual switching in motion integration

Perceptual multistability is a phenomenon in which alternate interpretations of a fixed stimulus are perceived intermittently. Although correlates between activity in specific cortical areas and perception have been found, the complex patterns of activity and the underlying mechanisms that gate multistable perception are little understood. Here, we present a neural field competition model in which competing states are represented in a continuous feature space. Bifurcation analysis is used to describe the different types of complex spatio-temporal dynamics produced by the model in terms of several parameters and for different inputs. The dynamics of the model was then compared to human perception investigated psychophysically during long presentations of an ambiguous, multistable motion pattern known as the barberpole illusion. In order to do this, the model is operated in a parameter range where known physiological response properties are reproduced whilst also working close to bifurcation. The model accounts for characteristic behaviour from the psychophysical experiments in terms of the type of switching observed and changes in the rate of switching with respect to contrast. In this way, the modelling study sheds light on the underlying mechanisms that drive perceptual switching in different contrast regimes. The general approach presented is applicable to a broad range of perceptual competition problems in which spatial interactions play a role.

Neuromechanistic Model of Auditory Bistability.

Sequences of higher frequency A and lower frequency B tones repeating in an ABA- triplet pattern are widely used to study auditory streaming. One may experience either an integrated percept, a single ABA-ABA- stream, or a segregated percept, separate but simultaneous streams A-A-A-A- and -B---B--. During minutes-long presentations, subjects may report irregular alternations between these interpretations. We combine neuromechanistic modeling and psychoacoustic experiments to study these persistent alternations and to characterize the effects of manipulating stimulus parameters. Unlike many phenomenological models with abstract, percept-specific competition and fixed inputs, our network model comprises neuronal units with sensory feature dependent inputs that mimic the pulsatile-like A1 responses to tones in the ABA- triplets. It embodies a neuronal computation for percept competition thought to occur beyond primary auditory cortex (A1). Mutual inhibition, adaptation and noise are implemented. We include slow NDMA recurrent excitation for local temporal memory that enables linkage across sound gaps from one triplet to the next. Percepts in our model are identified in the firing patterns of the neuronal units. We predict with the model that manipulations of the frequency difference between tones A and B should affect the dominance durations of the stronger percept, the one dominant a larger fraction of time, more than those of the weaker percept—a property that has been previously established and generalized across several visual bistable paradigms. We confirm the qualitative prediction with our psychoacoustic experiments and use the behavioral data to further constrain and improve the model, achieving quantitative agreement between experimental and modeling results. Our work and model provide a platform that can be extended to consider other stimulus conditions, including the effects of context and volition.

Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis

The existence of spatially localized solutions in neural networks is an important topic in neuroscience as these solutions are considered to characterize working (short-term) memory. We work with an unbounded neural network represented by the neural field equation with smooth firing rate function and a wizard hat spatial connectivity. Noting that stationary solutions of our neural field equation are equivalent to homoclinic orbits in a related fourth order ordinary differential equation, we apply normal form theory for a reversible Hopf bifurcation to prove the existence of localized solutions; further, we present results concerning their stability. Numerical continuation is used to compute branches of localized solution that exhibit snaking-type behaviour. We describe in terms of three parameters the exact regions for which localized solutions persist.

Localized radial bumps of a neural field equation on the Euclidean plane and the Poincaré disc

We analyse radially symmetric localized bump solutions of an integro-differential neural field equation posed in Euclidean and hyperbolic geometry. The connectivity function and the nonlinear firing rate function are chosen such that radial spatial dynamics can be considered. Using integral transforms, we derive a partial differential equation for the neural field equation in both geometries and then prove the existence of small amplitude radially symmetric spots bifurcating from the trivial state. Numerical continuation is then used to path follow the spots and their bifurcations away from onset in parameter space. It is found that the radial bumps in Euclidean geometry are linearly stable in a larger parameter region than bumps in the hyperbolic geometry. We also find and path follow localized structures that bifurcate from branches of radially symmetric solutions with D6-symmetry and D8-symmetry in the Euclidean and hyperbolic cases, respectively. Finally, we discuss the applications of our results in the context of neural field models of short term memory and edges and textures selectivity in a hypercolumn of the visual cortex.

Nonlinear Ground Dynamics of Aircraft: Bifurcation Analysis of Turning Solutions

During ground manoeuvres, particularly at high velocity when exiting the runway, a loss of lateral stability due to the saturation of the main landing gear tyres can cause the aircraft to enter a skid or a spin. The lateral stability is governed not only by aspects of the gear design, such as its geometry and tyre characteristics but also by operational variables, for example, the weather and taxiway condition. In this paper we develop an improved understanding and a new presentation of the dynamics of an aircraft manoeuvring on the ground, ultimately aimed at optimisation and automation of ground operations. Using a modified version of a nonlinear computer model of an A320 passenger aircraft developed by the Landing Gear Group at Airbus in the UK, we apply numerical continuation to investigate turning manoeuvres. We present a bifurcation analysis to describe the underlying structure that governs the dynamics of turning manoeuvres across the steering angle-thrust parameter space. There is a detailed description of the behaviour when lateral stability is lost using a novel diagrammatic approach to explain the dynamic tyre ground interactions. The bifurcation diagrams identify parameter regions for which this undesirable behaviour is avoidable and, thus, they form a foundation for defining the safe operating limits during turning manoeuvres.