Variations In Initial Conditions Research Articles

Breaking Bad: When Being Disadvantaged Incentivizes (Seemingly) Risky Behavior

We investigate how variation in initial conditions, which assign individuals into advantaged or disadvantaged positions, alters behavior. We illustrate the problem within a labor market context and consider the impact of accumulated debt on wage selectivity. Using a two-period model, we show that debt exerts a non-monotonic effect on wage selectivity, with agents assigned low and high levels of debt being significantly more likely to reject an initial wage offer than agents with moderate debt. This prediction is supported by our experiment, which finds a statistically significant dip in wage selectivity for subjects assigned moderate levels of debt.

Design of an Observer-Based Architecture and Non-Linear Control Algorithm for Cogging Torque Reduction in Synchronous Motors

The problem of cogging torque is due to a magnetic behavior, intrinsic to synchronous machines and due to the presence of permanent magnets themselves. Cogging torque is a significant problem when the servo drive is used for applications where high precision in terms of position control is required. In this paper we present a method of cogging torque reduction by means of a control technique based on mathematical modeling of the cogging phenomenon itself in order to exploit this knowledge directly in the controller design. The mathematical model is inserted in the dynamic model of the synchronous machine in order to exploit the feedback linearization, providing an expression of the control law in which the contribution of the deterministic knowledge of the phenomenon is directly present. The cogging phenomenon physically depends on the angular position of the rotor, as well as the deterministic model we use to define the control vector. This makes it interesting and innovative to determine whether the control algorithm can be inserted within a sensor-less architecture, where rotor position and angular velocity measurements are not available. For this purpose, we present the use of an extended Kalman filter (EKF) in the continuous-time domain, discussing the advantages of an observer design based on a dynamic motor model in three-phase and direct-square axes. Results are presented through very accurate simulation for a trajectory-tracking problem, completing with variational analysis in terms of variation of initial conditions between EKF and motor dynamics, and in terms of parametric variation to verify the robustness of the proposed algorithm. Moreover, a computational analysis based on Simulink Profiler is proposed, which provides some indication for possible implementation on an embedded platform.

Prescribed-time tracking for triangular systems of reaction-diffusion PDEs

Approximate controllability of systems of coupled parabolic partial differential equations has been of interest for a few decades, where the existence of open-loop control laws performing approximate state transitions within a finite time is studied. In this work, we specialize to systems of reaction-diffusion equations where the connectivity structure is triangular in the reaction parameters and the controls appear at the boundary. We first generate controllers by combining a decoupling backstepping approach with differential flatness that allow us to generate admissible trajectories for system outputs from a given initial condition. As a byproduct of our approach, we achieve approximate state transitioning for the system within a finite terminal time. We enhance our control law by introducing time-varying error feedback controllers which reject variations in initial conditions within the terminal time. The resulting control law not only performs the approximate control task but also output trajectory tracking, all within the terminal time which can be prescribed independently of initial conditions.

Complexity and Multistability in the Centrifugal Flywheel Governor System With Stochastic Noise

In this paper, dynamics and complexity of the integer-order and fractional-order centrifugal flywheel governor systems are investigated numerically by the bifurcation diagram, Lyapunov exponents (LCEs), chaos diagram and spectral entropy (SE) algorithm separately. Moreover, the effect of periodic force and stochastic noise on the dynamics and complexity of the integer-order and fractional-order systems also are analyzed. Finally, the multistability of the system is discussed by coexisting attractors and the basins of attraction. The results show that the fractional-order system has rich dynamical behaviours. Stochastic noise has a great effect on dynamics and complexity of the integer-order and fractional-order systems. The high complexity region is determined and SE complexity can indicate different state of the system effectively. And the integer-order and fractional-order systems show multistability with the variation of initial conditions.

Parametric investigation of the transition to turbulence in Rayleigh–Taylor mixing

A database is developed consisting of highly resolved large-eddy simulations of the transition process in a Rayleigh–Taylor mixing layer. Over 300 simulations are performed with parametric variations in Grashof number, Schmidt number, Atwood number, and initial perturbation spectrum. The database is then analyzed to explore how the factors that influence the transition-to-turbulence process impact mixing evolution and growth rate prior to the development of late-time, steady-state growth. The competition between entrainment-driven mixing and diffusion-driven mixing is observed, and two different mechanisms are suggested by which the homogeneity of mixing might increase, rather than decrease, at early time. The impact of parametric variation on growth rate is additionally examined, and all variations in initial conditions are found to converge to approximately the same growth parameter around α≈0.025.

A new fractional-order system displaying coexisting multiwing attractors; its synchronisation and circuit simulation

Abstract This paper presents a novel chaotic system having tan-hyperbolic non-linearity exhibiting chaotic attractors with multiple wings (2 or more) in its fractional-order dynamics. Also, there is coexistence of these strange attractors which has been proved by continuation method. The proposed system displays two types of multistability, one on variation of initial conditions and other on keeping the initial condition constant but varying the offset variable. The dynamical analysis of the system is done by comparison between the theoretical calculations and validation of simulated results. Adaptive sliding mode controller is applied to the system with disturbance for synchronisation. Feasibility of circuit implementation is also shown for the fractional-order representation of the system and possibility coexistence of attractors in terms of different initial condition and offset variable by means of circuit simulation.

Mechanism and sensitivity for broadband energy harvesting of an adaptive bistable point absorber wave energy converter

The adaptive bistable point absorber wave energy converter (WEC) concept proposed by Zhang et al. (Applied Energy 2018(228), pp. 450–467) is further investigated by exploring the underlying mechanism and sensitivity related to the broadband energy harvesting of this device. The mechanism can be explained in two different ways: (i) the broadband power capture is due to the fact that the adaptive bistable mechanism introduces both negative (at low wave frequencies) and positive (at high wave frequencies) stiffness to the device; and (ii) an inherent ‘phase control’ feature is observed especially at low wave frequency region. The variation of initial conditions of floater motion only has an observable influence at intermediate wave frequencies corresponding to chaotic response of the floater. The broad frequency bandwidth can be realized through different combinations of main and auxiliary springs' stiffness. The effects of wave amplitude on broadband energy harvesting can be categorized according to an optimum amplitude (if existing) into a gradual reduction for a larger wave amplitude and a quick drop for a smaller amplitude.

Homeorhesis and ecological succession quantified in synthetic microbial ecosystems

The dynamics of ecological change following a major perturbation, known as succession, are influenced by random processes. Direct quantitation of the degree of contingency in succession requires chronological study of replicate ecosystems. We previously found that population dynamics in carefully controlled, replicated synthetic microbial ecosystems were strongly deterministic over several months. Here, we present simplified, two-species microbial ecosystems consisting of algae and ciliates, imaged in toto at single-cell resolution with fluorescence microscopy over a period of 1 to 2 weeks. To directly study succession in these ecosystems, we deliberately varied the initial cell abundances over replicates and quantified the ensuing dynamics. The distribution of abundance trajectories rapidly converged to a nearly deterministic path, with small fluctuations, despite variations in initial conditions, environmental perturbations, and intrinsic noise, indicative of homeorhesis. Homeorhesis was also observed for certain phenotypic variables, such as partitioning of the ciliates into distinct size classes and clumping of the algae. Although the mechanism of homeorhesis observed in these synthetic ecosystems remains to be elucidated, it is clear that it must emerge from the ways each species controls its own internal states, with respect to a diverse set of environmental conditions and ecological interactions.

Extreme multistable synchronisation in coupled dynamical systems

A rule for designing extreme multistable synchronised systems by coupling two identical dynamical systems has been proposed in this paper. The basic idea behind the proposed scheme is the existence of chaos in the coupled system in the presence of initial condition-dependent constants of motion. A new conjecture has been introduced according to which an extreme multistable synchronised system can be designed if all states of one system will synchronise with the corresponding states of the other system (of the two coupled systems) and the basin of the synchronised state depends on the difference between the initial conditions of the corresponding states of the individual systems. The proposed scheme has been illustrated with the help of coupled Rossler systems, coupled Henon maps and coupled logistic maps. Moreover, the existence of flip bifurcation with the variation of initial conditions has been shown analytically as well as numerically in the case of coupled Henon maps. Numerical results are reported to show the proficiency of the proposed scheme to design extreme multistable synchronisation behaviour. This work establishes a theoretical foundation for constructing extreme multistable synchronised continuous as well as discrete dynamical systems.

Second-Order Trajectory Sensitivity Analysis of Hybrid Systems

Hybrid dynamical systems are characterized by intrinsic coupling between continuous dynamics and discrete events. This paper has adopted a differential-algebraic impulsive switched (DAIS) model to capture such dynamic behavior. For such systems, trajectory sensitivity analysis provides a valuable approach for describing perturbations of system trajectories resulting from small variations in initial conditions and/or uncertain parameters. The first-order sensitivities have been fully described for hybrid system and used in a variety of applications. This paper formulates the differential-algebraic equations (DAE) that govern second-order sensitivities over regions where dynamics are smooth, i.e., away from events. It also establishes the jump conditions that describe the step change in second-order sensitivities at discrete (switching and state reset) events. These results together fully characterize second-order sensitivities for general hybrid dynamical system.

Instability Resistance Training Decreases Motor Noise During Challenging Walking Tasks in Older Adults: A 10-Week Double-Blinded RCT.

Locomotor stability is challenged by internal perturbations, e.g., motor noise, and external perturbations, e.g., changes in surface compliance. One means to compensate for such perturbations is to employ motor synergies, defined here as co-variation among a set of elements that acts to stabilize, or provide similar trial-to-trial (or step-to-step) output, even in the presence of small variations in initial conditions. Whereas evidence exists that synergies related to the upper extremities can be trained, the extent to which lower limb synergies, such as those which may be needed to successfully locomote in complex environments, remains unknown. The purpose of this study was to evaluate if resistance training (RT) in unstable environments could promote coordination patterns associated with stronger synergies during gait. Sixty-eight participants between the age of 65 and 80 were randomly assigned to one of three different RT modalities: stable whole-limb machine-based RT (S-MRT), instability free-weight RT (I-FRT), and stable machine-based adductor/abductor RT (S-MRTHIP). Before and after RT, participants walked across an even lab floor and a more challenging uneven surface with and without holding a weighted bag. The uncontrolled manifold control analysis (UCM) was used to calculate the synergy index (i.e., strength of the kinematic synergy) related to stabilization of our performance variable, the mediolateral trajectory of the swing foot, under each condition. Regardless of RT group, there was no effect of RT on the synergy index when walking across the even lab floor. However, the synergy index during the two uneven surface conditions was stronger after I-FRT but was not affected by the other RT modalities. The stronger synergy index for the I-FRT group was due to improved coordination as quantified by an overall increase in variability in elemental variable space but a decrease in the variability that negatively affects performance. The unstable environment offered by I-FRT allows for exploration of motor solutions in a manner that appears to transfer to challenging locomotor tasks. Introducing tasks that promote, rather than limit, exploration of motor solutions seems to be a valuable exercise modality to strengthen kinematic synergies that cannot be achieved with traditional strengthening paradigms (e.g., S-MRT).Clinical Trial Registration: www.ClinicalTrials.gov, identifier NCT03017365.

Comparing Simple-radius and Doughnut Models of Collective Crowd Motion

In previous research, we developed an experiment-driven model of collective motion in human crowds (Warren, CDPS, in press). The behavioral dynamics model combines a local 'alignment' interaction, in which a pedestrian matches the speed and heading of a neighbor (Rio, Rhea, & Warren, 2014) with a neighborhood model, which computes a weighted average of multiple neighbors, with weights that decay exponentially with distance out to 4m (Warren & Dachner, VSS 2017; cf. Cuker & Smale, 2007). In addition, we found that the weight decreases more gradually with the distance to the nearest neighbor out to 11m (Wirth, Warren (& Richmond), VSS 2016), forming a larger doughnut-shaped neighborhood. Here we explore the model in multi-agent simulations, to determine the conditions under which it generates collective motion and to compare the simple-radius and doughnut neighborhoods. 30 interacting agents, with human parameters, were simulated on each 20s run, with synchronous updating. Their initial positions on a 5x6 grid were jittered, and initial conditions were parametrically varied: interpersonal distance (IPD=1-10m), heading range (±10° to ±90°), and speed range (±0.1 to ±0.9 m/s). There were 20 runs per condition, and the SD of final heading and speed were measured. The model converges to coherent motion over a wide range of initial headings and speeds, but less so as IPD increases. In addition, the number k of clusters of agents tends to increase with variation in initial conditions. Notably, the doughnut model converges over a larger range of conditions than the simple-radius model, providing a robust alternative to a 'topological' neighborhood that is not distance-dependent (Wirth & Warren, VSS 2018). We are currently comparing this physical model with a vision-based model driven by optical variables (Dachner & Warren, VSS 2017, 2018). Thus, the doughnut model generates collective motion that is robust to variation in initial conditions. Meeting abstract presented at VSS 2018

Stochastic Bistable Systems: Competing Hysteresis and Phase Coexistence

In this paper we describe the solution of a stochastic bistable system from a dynamical perspective. We show how a single framework with variable noise can explain hysteresis at zero temperature and two-state coexistence in the presence of noise. This feature is similar to the phase transition of thermodynamics. Our mathematical model for bistable systems also explains how the width of a hysteresis loop shrinks in the presence of noise, and how variation in initial conditions can take such systems to different final states.

Habitability of Exoplanet Waterworlds

Many habitable zone exoplanets are expected to form with water mass fractions higher than that of the Earth. For rocky exoplanets with 10-1000x Earth's H2O but without H2, we model the multi-Gyr evolution of ocean temperature and chemistry, taking into account C partitioning, high-pressure ice phases, and atmosphere-lithosphere exchange. Within our model, for Sun-like stars, we find that: (1)~the duration of habitable surface water is strongly affected by ocean chemistry; (2)~possible ocean pH spans a wide range; (3)~surprisingly, many waterworlds retain habitable surface water for >1 Gyr, and (contrary to previous claims) this longevity does not necessarily involve geochemical cycling. The key to this cycle-independent planetary habitability is that C exchange between the convecting mantle and the water ocean is curtailed by seafloor pressure on waterworlds, so the planet is stuck with the ocean mass and ocean cations that it acquires during the first 1% of its history. In our model, the sum of positive charges leached from the planetary crust by early water-rock interactions is - coincidentally - often within an order of magnitude of the early-acquired atmosphere+ocean inorganic C inventory overlaps. As a result, pCO2 is frequently in the "sweet spot" (0.2-20 bar) for which the range of semimajor axis that permits surface liquid water is about as wide as it can be. Because the width of the HZ in semimajor axis defines (for Sun-like stars) the maximum possible time span of surface habitability, this effect allows for Gyr of habitability as the star brightens. We illustrate our findings by using the output of an ensemble of N-body simulations as input to our waterworld evolution code. Thus (for the first time in an end-to-end calculation) we show that chance variation of initial conditions, with no need for geochemical cycling, can yield multi-Gyr surface habitability on waterworlds.

Interactively Learning a Blend of Goal-Based and Procedural Tasks

Agents that can learn new tasks through interactive instruction can utilize goal information to search for and learn flexible policies. This approach can be resilient to variations in initial conditions or issues that arise during execution. However, if a task is not easily formulated as achieving a goal or if the agent lacks sufficient domain knowledge for planning, other methods are required. We present a hybrid approach to interactive task learning that can learn both goal-oriented and procedural tasks, and mixtures of the two, from human natural language instruction. We describe this approach, go through two examples of learning tasks, and outline the space of tasks that the system can learn. We show that our approach can learn a variety of goal-oriented and procedural tasks from a single example and is robust to different amounts of domain knowledge.

Complex Dynamics in Arrays of Memristor Oscillators via the Flux–Charge Method

The key intent of the work is to analyze complex dynamics and synchronization phenomena in a 1-D array of $N$ diffusively coupled memristor-based oscillatory/chaotic circuits, i.e., each uncoupled oscillator is a 3rd–order memristor-based Chua’s circuit obtained by replacing the nonlinear resistor with an ideal flux-controlled memristor. It is shown that the state space $ \mathbb {R}^{4N}$ in the voltage–current domain of the array can be decomposed in $\infty ^{N}~3N$ -dimensional manifolds which are positively invariant for the nonlinear dynamics. Moreover, on each manifold the array obeys a different reduced-order dynamics in the flux-charge domain. These basic properties imply that two main types of bifurcations can occur, i.e., standard bifurcations on a fixed invariant manifold induced by changing the circuit parameters and bifurcations due to the variation of initial conditions and invariant manifold, but for fixed circuit parameters. The latter bifurcation phenomena are referred to as bifurcations without parameters. The reduced dynamics on invariant manifolds, and their analytic expressions, are the key tools for a comprehensive analysis of synchronization phenomena in the array of memristor-based Chua’s circuits. The main results are proved via a recently introduced technique for studying memristor-based circuits in the flux-charge domain.

Diverse self-organized patterns and complex pattern transitions in a discrete ratio-dependent predator–prey system

The spatiotemporal complexity of a discrete ratio-dependent predator–prey system is investigated via development of a coupled map lattice model. Through stability analysis and bifurcation analysis, the critical conditions for stable homogeneous stationary and oscillatory states are determined. Meanwhile, pattern formation conditions are derived by Turing instability analysis. Based on the theoretical results, numerical simulations are performed, exhibiting rich patterns of spatiotemporal dynamics of the discrete system. On the route to chaos induced by Neimark–Sacker bifurcation, dynamic variation occurs from invariant cycles, experiencing periodic window and period-doubling process, to chaotic attractors. A variety of patterns are self-organized and demonstrate diverse types in configuration, including cold spots, labyrinth, cold stripes-spots, spirals, hot stripes, circles, arcs, disk, mosaics and fractals. Complex pattern transitions occur among the diverse patterns, suggesting sensitivity of pattern formation to parameter variations. Moreover, spatiotemporal chaos is found in pattern formation process, where tiny variations in initial conditions can result to the self-organization of different patterns. This approach reveals great diversity and complexity of pattern self-organization and pattern transition in predator–prey interactions, promoting comprehending on the spatiotemporal complexity of spatially extended predator–prey system.

Importance of electron distribution profiles to chorus wave driven evolution of Jovian radiation belt electrons

Wave-particle interactions triggered by whistler-mode chorus waves are an important contributor to the Jovian radiation belt electron dynamics. While the sensitivity of chorus-driven electron scattering to the ambient magnetospheric and wave parameters has been investigated, there is rather limited understanding regarding the extent to which the dynamic evolution of Jovian radiation belt electrons, under the impact of chorus wave scattering, depends on the electron distribution profiles. We adopt a group of reasonable initial conditions based upon the available observations and models for quantitative analyses. We find that inclusion of pitch angle variation in initial conditions can result in increased electron losses at lower pitch angles and substantially modify the pitch angle evolution profiles of > ~500 keV electrons, while variations of electron energy spectrum tend to modify the evolution primarily of 1 MeV and 5 MeV electrons. Our results explicitly demonstrate the importance to the radiation belt electron dynamics in the Jovian magnetosphere of the initial shape of the electron phase space density, and indicate the extent to which variations in electron energy spectrum and pitch angle distribution can contribute to the evolution of Jovian radiation belt electrons caused by chorus wave scattering.

A scheme for designing extreme multistable discrete dynamical systems

In this paper, we propose a scheme for designing discrete extreme multistable systems coupling two identical dynamical systems. Existence of infinitely many attractors in the system is obtained via partial synchronization between two systems for a given set of parameters. We give a conjecture that extreme multistable systems can be designed by coupling two m-dimensional dynamical systems in such a way that i \((1 \le i\le m-1)\) number of state variables of the two systems synchronize completely and \((m-i)\) number of state variables keep constant difference. We demonstrate the applicability of our scheme in two-dimensional (2D) as well as three-dimensional (3D) discrete dynamical systems. In particular, we discuss our scheme taking coupled 2D Henon maps, coupled 2D Duffing maps and coupled 3D Henon maps. We have analytically shown the existence of fixed points and period-2 orbits in the coupled system with the variation of initial conditions. These analytically derived conditions matched very well with the numerical simulation results. Variation of the largest Lyapunov exponent with the initial conditions is shown to confirm the existence of extreme multistability in the model. Our scheme may be useful for designing physically, chemically and biologically useful multistable discrete dynamical systems.

Andronov-Hopf bifurcation with and without parameter in a cubic memristor oscillator with a line of equilibria.

The model of a memristor-based oscillator with cubic nonlinearity is studied. The considered system has infinitely many equilibrium points, which build a line of equilibria in the phase space. Numerical modeling of the dynamics is combined with the bifurcational analysis. It has been shown that the oscillation excitation has distinctive features of the supercritical Andronov-Hopf bifurcation and can be achieved by changing of a parameter value as well as by variation of initial conditions. Therefore, the considered bifurcation is called Andronov-Hopf bifurcation with and without parameter.