Impulsive Dynamics Research Articles

Bifurcations and chaos in the semi-passive bipedal dynamic walking model under a modified OGY-based control approach

This paper aims at investigating the semi-passive dynamic walking of a torso-driven biped robot under the Ott–Grebogi–Yorke (OGY) control approach as it goes down inclined planes. For the control, we used the desired torso angle as the accessible control parameter. Compared with our work in Gritli et al. (Nonlinear Dyn 79(2):1363–1384, 2015), a modified design of the OGY-based controller is proposed in this paper. Such controller is obtained by linearizing the impulsive hybrid nonlinear dynamics of the biped robot around a desired one-periodic hybrid limit cycle. Both the differential equation and the algebraic equation are linearized. As a result, we develop a simple mathematical expression of a controlled hybrid Poincare map. Determination of its fixed point and its Jacobian matrix requires only the knowledge of the nominal impact instant. We show efficiency of the designed OGY controller for the control of chaos in the impulsive hybrid nonlinear dynamics for some desired nominal values of the slope, and the desired torso angle. Furthermore, we analyzed via bifurcation diagrams the displayed behaviors in the controlled semi-passive biped robot as the slope parameter varies. We show the appearance of a Neimark–Sacker bifurcation and a cyclic-fold bifurcation, and also the exhibition of chaos. Our analysis of the controlled semi-passive gait is achieved also by means of the spectrum of Lyapunov exponents. Such study is realized via the controlled hybrid Poincare map where a reduction of its dimension is achieved.

Computation of the Lyapunov exponents in the compass-gait model under OGY control via a hybrid Poincaré map

This paper aims at providing a numerical calculation method of the spectrum of Lyapunov exponents in a four-dimensional impulsive hybrid nonlinear dynamics of a passive compass-gait model under the OGY control approach by means of a controlled hybrid Poincaré map. We present a four-dimensional simplified analytical expression of such hybrid map obtained by linearizing the uncontrolled impulsive hybrid nonlinear dynamics around a desired one-periodic passive hybrid limit cycle. In order to compute the spectrum of Lyapunov exponents, a dimension reduction of the controlled hybrid Poincaré map is realized. The numerical calculation of the spectrum of Lyapunov exponents using the reduced-dimension controlled hybrid Poincaré map is given in detail. In order to show the effectiveness of the developed method, the spectrum of Lyapunov exponents is calculated as the slope (bifurcation) parameter varies and hence used to predict the walking dynamics behavior of the compass-gait model under the OGY control.

The Role of the Media in De-Escalating Violent Conflicts in Nigeria

This paper examines the role of the media within the context of the very impulsive violent conflict dynamics in Nigeria. The paper constructs these dynamics from the backdrop of the country’s history in colonialism, which has shaped the contemporary narratives of the diverse socio-cultural nationalities as they relate with the state and among themselves. The paper employs the interdisciplinary methodology to review authoritative secondary literature to interpret primary sources on the evolution, character and manifestation of the media as it engages the Nigerian society. The paper finds that though the media is the product of the society, in this case the Nigerian society, it is evolving into a more responsive agent of social reengineering in line with global standard. Thus, the role of Nigerian media must not be viewed in isolation because of increasing acceleration of the forces of globalisation in permeating and penetrating the hitherto iron walls of national sovereignty and territorial integrity. Indeed, the Tower of Babel is here with us.

On Finite-Time Stability of Cyclic Switched Nonlinear Systems

This technical note considers the global finite-time stability problem for a class of switched nonlinear systems with the cyclic switching sequence, dissipative or non-dissipative impulsive effects may appear at each switching instant, and each mode may or may not be finite-time stable individually. A new concept named cycle dwell time is proposed based on which two stability conditions are established. These conditions fully reveal the trade-off among each mode's dynamics, impulsive dynamics and initial conditions. An example of multi-agent systems illustrates the efficiency of the new results.

An implicit systems characterization of a class of impulsive linear switched control processes. Part 2: Control

Our paper focuses on a fundamental structural property associated with a family of linear switched control systems in the presence of impulsive dynamics. We consider dynamic processes governed by piecewise linear ODEs with controlled location transitions. Using the newly developed implicit systems characterization technique, we rewrite the initially given impulsive switched system as an implicit dynamic model. This auxiliary representation of the original control system makes it possible to hide the switched phenomenon and to apply the conventional approach to the resulting implicit dynamic model. The proposed algebraic-based modeling framework follows the celebrated behavioral approach (see Polderman and Willems, 1998) and makes it possible to apply to the switched dynamics some classic techniques from the well-established time-invariant implicit systems theory. The analytic results of our paper constitute a formal theoretical extension of switched control systems methodology and can be used (as an auxiliary step) in a concrete control design procedure. The second part of our manuscript is devoted to control aspects.

Cardiac Vagal Afferent Response in Rats during Cardiac Contractility Modulation (CCM)

Congestive heart failure (CHF) is responsible for substantial cardiac morbidity and mortality. Cardiac Contractility Modulation (CCM) delivers non‐excitatory endocardial electrical pulses during the refractory period. CCM enhances cardiac contractility, ejection fraction, and quality of life in patients. The underlying mechanism of action for these benefits is not fully understood. Since similar impulses delivered to the gut increase muscle contraction leading to activation of vagal afferents, we tested the effect of CCM on vagal afferent activity in the heart.HypothesisCCM results in an increase in activity of cardiac vagal afferent nerves. Since CCM is non‐excitatory, we speculate that CCM reflexly activates vagal afferents via increases in contractility, reducing excessive efferent sympathetic tone in CHF.MethodsAdult male Sprague‐Dawley rats under pentobarbital anesthesia were instrumented for extracellular recordings of cardiac vagal afferent firing during CCM stimulation of the left ventricle (4V or 7.5V for 60s).ResultsIn 18 vagal nerve fibers with cardiac receptive fields, CCM produced an intensity dependent increase (p<0.05) in firing frequency of 10 fibers (4.2 ± 1.2 Hz at 7.5V vs. 1.4 ± 0.66 Hz at baseline). 6 neurons were not affected by CCM. In two neurons, 4V stimulation increased while 7.5V had no effect on single fiber firing.ConclusionCCM, a new therapy for CHF elicits activation of cardiac vagal afferents. This likely results from a reflex increase in regional contractility, contributing to the clinical benefit of CCM via an increase in vagal afferent and reduced sympathetic tone. Supported by Impulse Dynamics, Inc.

Invariant sets for the nonlinear impulsive control systems

The nonlinear impulsive control system with trajectories of bounded variation is considered. The notions of strong and weak V-invariance of a closed set relative to the impulsive control system are introduced. These notions are adapted to the system nonautonomy in the so-called "fast" time, in which the impulsive dynamics occurs. Invariance criteria in the form of the proximal Hamilton-Jacobi equalities were proved.

Interface nano-confined acoustic waves in polymeric surface phononic crystals

The impulsive acoustic dynamics of soft polymeric surface phononic crystals is investigated here in the hypersonic frequency range by near-IR time-resolved optical diffraction. The acoustic response is analysed by means of wavelet spectral methods and finite element modeling. An unprecedented class of acoustic modes propagating within the polymer surface phononic crystal and confined within 100 nm of the nano-patterned interface is revealed. The present finding opens the path to an alternative paradigm for characterizing the mechanical properties of soft polymers at interfaces and for sensing schemes exploiting polymers as embedding materials.

SPH Based Approach toward the Simulation of Non-cohesive Sediment Removal by an Innovative Technique Using a Controlled Sequence of Underwater Micro-explosions

This paper shows an advanced application of the SPHERA code, a SPH-based numerical model, for simulating the impulsive dynamics of a multiphase system. The final purpose is to set up a numerical model for the development of an innovative technique that could be applied to increase the effectiveness of non-cohesive sediment removal at the bottom of an artificial reservoir through the combined use of submerged micro-explosions and flushing maneuvers. Experimental tests have been carried out to support the study and to provide a data set for model calibration and validation. Since the use of an explosive charge requires special and expensive safety measures, at this stage of investigation micro-explosions are mimed by means of the injection of a cold CO2 pressurized gas from the bottom of a 2D laboratory tank containing water and a sand bed at initial rest condition: even if this represents a strong simplification, the experiments were carried out to provide a first insight in the physics of the water-sediment impulsive dynamics including some similarities with the underwater explosion inside a non-cohesive sediment layer at rest (inertial effects dominate). Even if some improvements of the model are required to reach the final purpose, the results show both good qualitative agreement with the experimental frames and the capability of the SPHERA code to support further investigations that are necessary to understand the real feasibility of this removal technique and to optimize the times and locations of injections/explosions in order to improve the efficiency of sediment flushing.

Invariant Solutions of Differential Games with Measures: A Discontinuous Time Reparameterization Approach

The paper is devoted to bilevel qualitative games with impulsive dynamics described by a measure differential equation. We study games with fixed impulses, and games with impulsive control in the hands of the lower level player, provided that the upper level player aims to ensure the existence of invariant solutions to a measure differential equation under any admissible answer of the opponent. We give sufficient conditions for weak invariance of time-varying domains with respect to the impulsive dynamical games.

Molecular dynamics simulation of square graphene-nanoflake oscillator on graphene nanoribbon.

Graphene nanoflakes (GNFs) have been of interest for a building block in order to develop electromechanical devices on a nanometer scale. Here, we present the oscillation motions of a square GNF oscillator on graphene nanoribbon (GNR) in the retracting-motions by performing classical molecular dynamics simulations. The simulation results showed that the GNF oscillators can be considered as a building block for nanoelectromechanical systems such as carbon-nanotube (CNT) oscillators. The oscillation dynamics of the GNF oscillator were similar to those of the CNT oscillators. When the square GNF had an initial velocity as impulse dynamics, its oscillation motions on the GNR were achieved from its self-retracting van der Waals force. For low initial velocity, its translational motions were dominant in its motions rather than its rotational motions. The kinetic energy damping ratio rapidly decreased as initial velocity increased and the kinetic energy for the translational motion of the GNF oscillator rapidly transferred into that for its rotational motion. The oscillation frequency of the GNF oscillator was dependent on its initial velocity.

Pain as a Conversion Symptom or a Psychosomatic Phenomenon: Fake or Real?

According to the psychoanalytical Freudian approach, the pain in a conversion symptom (hysterical pain), whether defined or indefinable, corresponds to a displacement of the intrapsychic conflict to the subject’s physical body. The libidinal energy attached to the repressed representation is transformed into neurotic energy in organs or parts of the body so as to dramatically represent the desirable as well as the prohibitive. The body lends itself as a ‘location’ to the conversion disorder in order for the anguish of the intrapsychic conflict to be expressed in openly manipulative terms. Does this hysterical pain designate both the pleasure of the performance and the discontent of the psychological anguish? On the contrary, the psychosomatic pain manifests itself in the actual physical body of the organism and not in the illusory body of the hysteric. It is possible for the (psycho)somatic disorder to be expressed through the pain symptom upon an existing, objective condition diagnosed in an organ or body part. But is it not the very nature of the psychosomatic disorder a unique differentiation criterion between the two types of the disorder? The rationale, the type of the psychological defense mechanisms and the nature of the impulsive dynamics which subdue each of those two types of painful symptoms constitute criteria of other differentiators within the psychopathological and psychoanalytic approach.

An investigation of systemic stress and interdependencies within the Eurozone and Euro Area countries

One of the most challenging issues that economists are dealing with is the investigation of the financial turmoil in Eurozone economies. Particularly, the issue of exposing the potential crisis transmission channels has attracted considerable interest. Aiming to contribute to this literature, we construct financial stress indices on a country level and explore further the potential inter-reactions between the root causes of systemic risk. The country-specific index consists of a wide number of series drawn from the money, equity and bond markets, as well as from the banking sector of each Eurozone country. A Euro Area stress index is also provided, exploring the evolution of financial conditions for this group of countries. The investigation of the potential transmission channels is implemented through a multivariate analysis and the corresponding impulse responses' dynamics. The empirical findings suggest that countries are mostly responsive to their own financial shocks, while a degree of regionalism is also evident. That is, the peripheral countries are more susceptible to their financial stress, while the same holds for the core Eurozone countries. Additionally, in contrast to common wisdom, financial conditions in Greece and Portugal do not seem to affect the rest of the Euro Area, at least in the degree that Italy and Ireland do. These results are consistent under alternative model and sample specifications.

OGY-based control of chaos in semi-passive dynamic walking of a torso-driven biped robot

This paper aims at controlling chaos exhibited in the semi-passive dynamic walking of a torso-driven biped robot as it goes down an inclined surface. Our control approach is based on the OGY method. The proposed biped robot is a three-degrees-of-freedom planar biped having an impulsive hybrid nonlinear dynamics. For this walker, we use only one torque between the stance leg and the torso in order to control the torso at some desired position and then in order to generate a semi-passive gait. The desired torso angle is considered as the control parameter in our OGY-based control approach. We develop a reduced simple impulsive hybrid linear model by linearizing the impulsive hybrid nonlinear dynamics around a desired period-1 hybrid limit cycle. This conducts to determine an explicit expression of a constrained controlled Poincare map. A linearization of the controlled Poincare map around its fixed point permits to looking for the gain matrix of the stabilizing control law. We show that application of the developed OGY-based control parameter law has controlled the chaotic semi-passive gait.

Molecular dynamics study on the C60 oscillator in a graphene nanoribbon trench

Here, we present a C60 oscillator encapsulated in a graphene nanoribbon (GNR) trench. The mechanisms of the C60/GNR-trench oscillators are the same as those of the multi-walled carbonnanotube (CNT) oscillators. While the array synthesis of these CNT oscillators is very difficult, the same GNR trench array can be implemented by using current nanofabrication processes. The oscillatory behaviors of a C60 oscillator sucked into a GNR trench were investigated in impulse dynamics via classical molecular dynamics simulations. The oscillatory motions of the C60 oscillator in the GNR trench can be controlled by using the length and the width of the trench as structural parameters because the restoring forces acting on the C60 oscillator are related to the width of the GNR trench and the length of the GNR trench is the direct distance of motion of the C60 oscillator during translation. C60/GNR-trench nanostructures have a wide range of applications in nanotechnology, such as shuttle memories and switches, sensors, and oscillators.

Imaging feedback for histotripsy by characterizing dynamics of acoustic radiation force impulse (ARFI)-induced shear waves excited in a treated volume.

Our previous study indicated that shear waves decay and propagate at a lower speed as they propagate into a tissue volume mechanically fractionated by histotripsy. In this paper, we hypothesize that the change in the shear dynamics is related to the degree of tissue fractionation, and can be used to predict histotripsy treatment outcomes. To test this hypothesis, lesions with different degrees of tissue fractionation were created in agar-graphite tissue phantoms and ex vivo kidneys with increasing numbers of therapy pulses, from 0 to 2000 pulses per treatment location. The therapy pulses were 3-cycle 750-kHz focused ultrasound delivered at a peak negative/positive pressure of 17/108 MPa and a repetition rate of 50 Hz. The shear waves were excited by acoustic radiation force impulse (ARFI) focused at the center of the lesion. The spatial and temporal behavior of the propagating shear waves was measured with ultrasound plane wave imaging. The temporal displacement profile at a lateral location 10 mm offset to the shear excitation region was detected with M-mode imaging. The decay and delay of the shear waves were quantitatively characterized on the temporal displacement profile. Results showed significant changes in two characteristics on the temporal displacement profile: the peak-to-peak displacement decayed exponentially with increasing numbers of therapy pulses; the relative time-to-peak displacement increased with increasing numbers of therapy pulses, and appeared to saturate at higher numbers of pulses. Correspondingly, the degree of tissues fractionation, as indicated by the percentage of structurally intact cell nuclei, decreased exponentially with increasing numbers of therapy pulses. Strong linear correlations were found between the two characteristics and the degree of tissue fractionation. These results suggest that the characteristics of the shear temporal displacement profile may provide useful feedback information regarding the treatment outcomes.

An implicit systems characterization of a class of impulsive linear switched control processes. Part 1: Modeling

Our paper focuses on a fundamental structural property associated with a family of linear switched control systems in the presence of impulsive dynamics. We consider dynamic processes governed by piecewise linear ODEs with controlled location transitions and describe the resulting system in a constructive form of an implicit dynamic system. The proposed algebraic-based modeling framework follows the celebrated behavioral approach (see Polderman and Willems (1998)) and makes it possible to apply to the switched dynamics some conventional techniques from the well-established time-invariant implicit systems theory. The analytic results of our paper constitute a formal theoretical extension of switched control systems methodology and can be used (as an auxiliary step) in a concrete control design procedure. In this first part, we consider modeling aspects.

Artifact Removal from Single-Trial ERPs using Non-Gaussian Stochastic Volatility Models and Particle Filter

This paper considers improved modeling of artifactual noise for denoising of single-trial event-related potentials (ERPs) by state-space approach. Instead of the inadequate constant variance models used in existing studies, we propose to use stochastic volatility (SV) models to better describe the time-varying volatility in real ERP noise sources. We further propose a class of non-Gaussian SV models to capture the abrupt volatility changes typically present in impulsive noise, to improve artifact removal from ERPs. Two specifications are considered: (1) volatility driven by a heavy-tailed component and (2) transformation of volatility. Both result in volatility processes with heavy-tailed transition densities which can predict the impulsive noise volatility dynamics, more accurately than the Gaussian models. These SV noise models are incorporated in an autoregressive (AR) state-space ERP dynamic model. Parameter estimation is done using a Rao-Blackwellized particle filter (RBPF). Evaluation on simulated auditory brainstem responses (ABRs), corrupted by real eye-blink artifacts, shows that the non-Gaussian models can accurately detect the artifact-induced abrupt volatility spikes, and able to uncover the underlying inter-trial dynamics. Among them, the log-SV model performs the best. The results on real data demonstrate significant artifact suppression.

On the impulsive dynamics of M-blocks

This paper is concerned with the motion of a cubic rigid body (cube) with a rotor, caused by a sudden brake of the rotor, which imparts its angular momentum to the body. This produces an impulsive reaction of the support, leading to a jump or rolling from one face to another. Such dynamics was demonstrated by researchers from Massachusetts Institute of Technology at the IEEE/RSJ International Conference on Intelligent Robots and Systems in Tokio in November 2013. The robot, called by them M-block, is 4 cm in size and uses an internal flywheel mechanism rotating at 20 000 rev/min. Initially the cube rests on a horizontal plane. When the brake is set, the relative rotation slows down, and its energy is imparted to the case. The subsequent motion is illustrated in a clip [13]. Here the general approach to the analysis of dynamics of M-cube is proposed, including equations of impulsive motion and methods of their solution. Some particular cases are studied in details.

Sustained High-Frequency Dynamic Instability of a Nonlinear System of Coupled Oscillators Forced by Single or Repeated Impulses: Theoretical and Experimental Results

This report describes the impulsive dynamics of a system of two coupled oscillators with essential (nonlinearizable) stiffness nonlinearity. The system considered consists of a grounded weakly damped linear oscillator coupled to a lightweight weakly damped oscillating attachment with essential cubic stiffness nonlinearity arising purely from geometry and kinematics. It has been found that under specific impulse excitations the transient damped dynamics of this system tracks a high-frequency impulsive orbit manifold (IOM) in the frequency-energy plane. The IOM extends over finite frequency and energy ranges, consisting of a countable infinity of periodic orbits and an uncountable infinity of quasi-periodic orbits of the underlying Hamiltonian system and being initially at rest and subjected to an impulsive force on the linear oscillator. The damped nonresonant dynamics tracking the IOM then resembles continuous resonance scattering; in effect, quickly transitioning between multiple resonance captures over finite frequency and energy ranges. Dynamic instability arises at bifurcation points along this damped transition, causing bursts in the response of the nonlinear light oscillator, which resemble self-excited resonances. It is shown that for an appropriate parameter design the system remains in a state of sustained high-frequency dynamic instability under the action of repeated impulses. In turn, this sustained instability results in strong energy transfers from the directly excited oscillator to the lightweight nonlinear attachment; a feature that can be employed in energy harvesting applications. The theoretical predictions are confirmed by experimental results.