Aperiodic Dynamics Research Articles

EEG aperiodic dynamics from early through late childhood: Associations with ADHD, cognition, and development

BackgroundAperiodic resting electroencephalography (EEG) activity is dynamic, reflecting shifting excitatory:inhibitory (E:I) balance with changing environmental conditions. We examined developmental and cognitive correlates of aperiodic and dynamic aperiodic indices in a cross-sequential cohort of early, middle, and late childhood youth with and without attention deficit hyperactivity disorder (ADHD). MethodsTwo-hundred eighty-five children ages 2 – 14 years provided resting EEG during high- and low-visual input conditions. Licensed clinical psychologists determined ADHD diagnosis or likelihood (in young children). Linear regressions were estimated to examine associations between aperiodic features and age, ADHD diagnosis, IQ, and experimental condition. ResultsFrom early to middle childhood, the aperiodic exponent increased linearly, indicating lower E:I, followed by a decreasing trajectory in late childhood. The aperiodic exponent was greater with high versus low visual input in young children, but this effect reversed with age. The ADHD group had a decreased aperiodic exponent, overall. Dynamic aperiodic activity, i.e. shifts in E:I balance, was associated with IQ. ConclusionsThe aperiodic exponent and aperiodic dynamics are proxies for age-related cortical maturation and E:I balance, and have distinct associations with ADHD symptoms and cognitive ability. SignificanceWe provide novel evidence that dynamic aperiodic activity is a candidate marker of cortical efficiency in childhood.

Differential effects of haloperidol on neural oscillations during wakefulness and sleep

The electrical activity of the brain, characterized by its frequency components, reflects a complex interplay between periodic (oscillatory) and aperiodic components. These components are associated with various neurophysiological processes, such as the excitation-inhibition balance (aperiodic activity) or interregional communication (oscillatory activity). However, we do not fully understand whether these components are truly independent or if different neuromodulators affect them in different ways. The dopaminergic system has a critical role for cognition and motivation, being a potential modulator of these power spectrum components. To improve our understanding of these questions, we investigated the differential effects of this system on these components using electrocorticogram recordings in cats, which show clear oscillations and aperiodic 1/f activity. Specifically, we focused on the effects of haloperidol (a D2 receptor antagonist) on oscillatory and aperiodic dynamics during wakefulness and sleep. By parameterizing the power spectrum into these two components, our findings reveal a robust modulation of oscillatory activity by the D2 receptor across the brain. Surprisingly, aperiodic activity was not significantly affected and exhibited inconsistent changes across the brain. This suggests a nuanced interplay between neuromodulation and the distinct components of brain oscillations, providing insights into the selective regulation of oscillatory dynamics in awake states.

Dynamic behavior and driving region of spray combustion instability in a backward-facing step combustor.

We numerically study the dynamic behavior and driving region of spray combustion instability in a backward-facing step combustor using analytical methodologies based on dynamical systems theory, symbolic dynamics, complex networks, and machine learning. The global dynamic behavior of a heat release rate field represents low-dimensional chaotic oscillations with deterministically aperiodic intercycle dynamics. Spray combustion instability is driven in the formation and separation region of a large-scale organized vortex induced by the hydrodynamic shear layer instability at the edge of the backstep. This region corresponds fairly to that of the hub in an acoustic-energy-flux-based spatial network. The feature importance in a random forest is valid for clarifying the feedback coupling of spray combustion instability.

River Ecomorphodynamic Models Exhibit Features of Nonlinear Dynamics and Chaos

AbstractModeling the nonlinear interactions between flow, sediment, and vegetation is essential for improving our understanding and prediction of river system dynamics. Using simple numerical models, we simulate the key flow‐sediment‐vegetation interaction where the disturbance is intrinsically generated by the presence of vegetation. In this case, biomass growth modifies the flow field, induces bed scour, and thus potentially causes vegetation uprooting when erosion exceeds root depth. Our results show that this nonlinear feedback produces deterministic chaos under a wide range of conditions, with complex aperiodic dynamics generated by a period‐doubling route to chaos. Moreover, our results suggest relatively small values of Lyapunov time, spanning 2–4 growth‐flood cycles, which significantly restrict the predictability of riverbed evolution. Although further spatial and temporal processes may add complexity to the system, these results call for the use of ensemble methods and associated uncertainty estimates in ecomorphodynamic models.

Chimera dynamics of generalized Kuramoto–Sakaguchi oscillators in two-population networks

Chimera dynamics, an intriguing phenomenon of coupled oscillators, is characterized by the coexistence of coherence and incoherence, arising from a symmetry-breaking mechanism. Extensive research has been performed in various systems, focusing on a system of Kuramoto–Sakaguchi (KS) phase oscillators. In recent developments, the system has been extended to the so-called generalized Kuramoto model, wherein an oscillator is situated on the surface of an M-dimensional unit sphere, rather than being confined to a unit circle. In this paper, we exploit the model introduced in Tanaka (2014 New. J. Phys. 16 023016) where the macroscopic dynamics of the system was studied using the extended Watanabe–Strogatz transformation both for real and complex spaces. Considering two-population networks of the generalized KS oscillators in 2D complex spaces, we demonstrate the existence of chimera states and elucidate different motions of the order parameter vectors depending on the strength of intra-population coupling. Similar to the KS model on the unit circle, stationary and breathing chimeras are observed for comparatively strong intra-population coupling. Here, the breathing chimera changes their motion upon decreasing intra-population coupling strength via a global bifurcation involving the completely incoherent state. Beyond that, the system exhibits periodic alternation of the two order parameters with weaker coupling strength. Moreover, we observe that the chimera state transitions into a componentwise aperiodic dynamics when the coupling strength weakens even further. The aperiodic chimera dynamics emerges due to the breaking of conserved quantities that are preserved in the stationary, breathing and alternating chimera states. We provide a detailed explanation of this scenario in both the thermodynamic limit and for finite-sized ensembles. Furthermore, we note that an ensemble in 4D real spaces demonstrates similar behavior.

Emergent programmable behavior and chaos in dynamically driven active filaments

How the behavior of cells emerges from their constituent subcellular biochemical and physical parts is an outstanding challenge at the intersection of biology and physics. A remarkable example of single-cell behavior occurs in the ciliate Lacrymaria olor, which hunts for its prey via rapid movements and protrusions of a slender neck, many times the size of the original cell body. The dynamics of this cell neck is powered by a coat of cilia across its length and tip. How a cell can program this active filamentous structure to produce desirable behaviors like search and homing to a target remains unknown. Here, we present an active filament model that allows us to uncover how a "program" (time sequence of active forcing) leads to "behavior" (filament shape dynamics). Our model captures two key features of this system-time-varying activity patterns (extension and compression cycles) and active stresses that are uniquely aligned with the filament geometry-a "follower force" constraint. We show that active filaments under deterministic, time-varying follower forces display rich behaviors including periodic and aperiodic dynamics over long times. We further show that aperiodicity occurs due to a transition to chaos in regions of a biologically accessible parameter space. We also identify a simple nonlinear iterated map of filament shape that approximately predicts long-term behavior suggesting simple, artificial "programs" for filament functions such as homing and searching space. Last, we directly measure the statistical properties of biological programs in L. olor, enabling comparisons between model predictions and experiments.

Chaotic chimera attractors in a triangular network of identical oscillators.

A prominent type of collective dynamics in networks of coupled oscillators is the coexistence of coherently and incoherently oscillating domains known as chimera states. Chimera states exhibit various macroscopic dynamics with different motions of the Kuramoto order parameter. Stationary, periodic and quasiperiodic chimeras are known to occur in two-population networks of identical phase oscillators. In a three-population network of identical Kuramoto-Sakaguchi phase oscillators, stationary and periodic symmetric chimeras were previously studied on a reduced manifold in which two populations behaved identically [Phys. Rev. E 82, 016216 (2010)1539-375510.1103/PhysRevE.82.016216]. In this paper, we study the full phase space dynamics of such three-population networks. We demonstrate the existence of macroscopic chaotic chimera attractors that exhibit aperiodic antiphase dynamics of the order parameters. We observe these chaotic chimera states in both finite-sized systems and the thermodynamic limit outside the Ott-Antonsen manifold. The chaotic chimera states coexist with a stable chimera solution on the Ott-Antonsen manifold that displays periodic antiphase oscillation of the two incoherent populations and with a symmetric stationary chimera solution, resulting in tristability of chimera states. Of these three coexisting chimera states, only the symmetric stationary chimera solution exists in the symmetry-reduced manifold.

Decreased aperiodic neural activity in Parkinson's disease and dementia with Lewy bodies.

Neural oscillations and signal complexity have been widely studied in neurodegenerative diseases, whereas aperiodic activity has not been explored yet in those disorders. Here, we assessed whether the study of aperiodic activity brings new insights relating to disease as compared to the conventional spectral and complexity analyses. Eyes-closed resting-state electroencephalography (EEG) was recorded in 21 patients with dementia with Lewy bodies (DLB), 28 patients with Parkinson's disease (PD), 27 patients with mild cognitive impairment (MCI) and 22 age-matched healthy controls. Spectral power was differentiated into its oscillatory and aperiodic components using the Irregularly Resampled Auto-Spectral Analysis. Signal complexity was explored using the Lempel-Ziv algorithm (LZC). We found that DLB patients showed steeper slopes of the aperiodic power component with large effect sizes compared to the controls and MCI and with a moderate effect size compared to PD. PD patients showed steeper slopes with a moderate effect size compared to controls and MCI. Oscillatory power and LZC differentiated only between DLB and other study groups and were not sensitive enough to detect differences between PD, MCI, and controls. In conclusion, both DLB and PD are characterized by alterations in aperiodic dynamics, which are more sensitive in detecting disease-related neural changes than the traditional spectral and complexity analyses. Our findings suggest that steeper aperiodic slopes may serve as a marker of network dysfunction in DLB and PD features.

Heteroclinic cycling and extinction in May–Leonard models with demographic stochasticity

May and Leonard (SIAM J Appl Math 29:243–253, 1975) introduced a three-species Lotka–Volterra type population model that exhibits heteroclinic cycling. Rather than producing a periodic limit cycle, the trajectory takes longer and longer to complete each “cycle”, passing closer and closer to unstable fixed points in which one population dominates and the others approach zero. Aperiodic heteroclinic dynamics have subsequently been studied in ecological systems (side-blotched lizards; colicinogenic Escherichia coli), in the immune system, in neural information processing models (“winnerless competition”), and in models of neural central pattern generators. Yet as May and Leonard observed “Biologically, the behavior (produced by the model) is nonsense. Once it is conceded that the variables represent animals, and therefore cannot fall below unity, it is clear that the system will, after a few cycles, converge on some single population, extinguishing the other two.” Here, we explore different ways of introducing discrete stochastic dynamics based on May and Leonard’s ODE model, with application to ecological population dynamics, and to a neuromotor central pattern generator system. We study examples of several quantitatively distinct asymptotic behaviors, including total extinction of all species, extinction to a single species, and persistent cyclic dominance with finite mean cycle length.

Spectral slowing in chronic stroke reflects abnormalities in both periodic and aperiodic neural dynamics

Decades of electrophysiological work have demonstrated the presence of “spectral slowing” in stroke patients – a prominent shift in the power spectrum towards lower frequencies, most evident in the vicinity of the lesion itself. Despite the reliability of this slowing as a marker of dysfunctional tissue across patient groups as well as animal models, it has yet to be explained in terms of the pathophysiological processes of stroke. To do so requires clear understanding of the neural dynamics that these differences represent, acknowledging the often overlooked fact that spectral power reflects more than just the amplitude of neural oscillations. To accomplish this, we used a combination of frequency domain and time domain measures to disambiguate and quantify periodic (oscillatory) and aperiodic (non-oscillatory) neural dynamics in resting state magnetoencephalography (MEG) recordings from chronic stroke patients. We found that abnormally elevated low frequency power in these patients was best explained by a steepening of the aperiodic component of the power spectrum, rather than an enhancement of low frequency oscillations, as is often assumed. However, genuine oscillatory activity at higher frequencies was also found to be abnormal, with patients showing alpha slowing and diminished oscillatory activity in the beta band. These aperiodic and periodic abnormalities were found to covary, and could be detected even in the un-lesioned hemisphere, however they were most prominent in perilesional tissue, where their magnitude was predictive of cognitive impairment. This work redefines spectral slowing as a pattern of changes involving both aperiodic and periodic neural dynamics and narrows the gap in understanding between non-invasive markers of dysfunctional tissue and disease processes responsible for altered neural dynamics.

The role of aperiodic spectral slope in event-related potentials and cognition among children with and without attention deficit hyperactivity disorder.

Aperiodic spectral slope is a measure of spontaneous neural oscillatory activity that is believed to support regulation of brain responses to environmental stimuli. Compared to typically developing (TD) control participants, children with attention deficit hyperactivity disorder (ADHD) have been shown to have flatter aperiodic spectral slope at rest as well as attenuated event-related potential (ERP) amplitudes in response to environmental stimuli. A small body of research suggests that aperiodic slope may also explain differences in behavioral responses. In this study, we examine associations between prestimulus aperiodic slope, stimulus characteristics, environmental demands, and neural as well as behavioral responses to these stimuli. Furthermore, we evaluate whether ADHD diagnostic status moderates these associations. Seventy-nine children with ADHD and 27 TD school-age children completed two visual ERP experiments with predictable alternating presentations of task-relevant and task-irrelevant stimuli. Aperiodic slope was extracted from prestimulus time windows. Prestimulus aperiodic slope was steeper for the TD relative to ADHD group, driven by task-relevant rather than task-irrelevant stimuli. For both groups, the aperiodic slope was steeper during a task with lower cognitive demand and before trials in which they responded correctly. Aperiodic slope did not mediate the association between ADHD diagnosis and attenuated P300 amplitude. The aperiodic spectral slope is dynamic and changes in anticipation of varying stimulus categories to support performance. The aperiodic slope and P300 amplitude reflect distinct cognitive processes. Background neural oscillations, captured via aperiodic slope, support cognitive behavioral control and should be included in etiological models of ADHD.NEW & NOTEWORTHY This study constitutes the first investigation of associations between aperiodic spectral slope and three aspects of neurocognition: event-related potential (ERP) amplitudes, cognitive load, and task performance. We find that background oscillatory activity is dynamic, shifting in anticipation of varying levels of task relevance and in response to increasing cognitive load. Moreover, we report that aperiodic activity and ERPs constitute distinct neurophysiological processes. Children with attention deficit hyperactivity disorder (ADHD) show reduced aperiodic dynamics in addition to attenuated ERP amplitudes.

Time-resolved parameterization of aperiodic and periodic brain activity.

Macroscopic neural dynamics comprise both aperiodic and periodic signal components. Recent advances in parameterizing neural power spectra offer practical tools for evaluating these features separately. Although neural signals vary dynamically and express non-stationarity in relation to ongoing behaviour and perception, current methods yield static spectral decompositions. Here, we introduce Spectral Parameterization Resolved in Time (SPRiNT) as a novel method for decomposing complex neural dynamics into periodic and aperiodic spectral elements in a time-resolved manner. First, we demonstrate, with naturalistic synthetic data, SPRiNT's capacity to reliably recover time-varying spectral features. We emphasize SPRiNT's specific strengths compared to other time-frequency parameterization approaches based on wavelets. Second, we use SPRiNT to illustrate how aperiodic spectral features fluctuate across time in empirical resting-state EEG data (n=178) and relate the observed changes in aperiodic parameters over time to participants' demographics and behaviour. Lastly, we use SPRiNT to demonstrate how aperiodic dynamics relate to movement behaviour in intracranial recordings in rodents. We foresee SPRiNT responding to growing neuroscientific interests in the parameterization of time-varying neural power spectra and advancing the quantitation of complex neural dynamics at the natural time scales of behaviour.

Generation of aperiodic motion due to sporadic collisions of camphor ribbons.

We present numerical and experimental results for the generation of aperiodic motion in coupled active rotators. The numerical analysis is presented for two point particles constrained to move on a unit circle under the Yukawa-like interaction. Simulations exhibit that the collision among the rotors results in chaotic motion of the rotating point particles. Furthermore, the numerical model predicts a route to chaotic motion. Subsequently, we explore the effect of separation between the rotors on their chaotic dynamics. The numerically calculated fraction of initial conditions which led to chaotic motion shed light on the observed effects. We reproduce a subset of the numerical observations with two self-propelled ribbons rotating at the air-water interface. A pinned camphor rotor moves at the interface due to the Marangoni forces generated by surface tension imbalance around it. The camphor layer present at the common water surface acts as chemical coupling between two ribbons. The separation distance of ribbons (L) determines the nature of coupled dynamics. Below a critical distance (L_{T}), rotors can potentially, by virtue of collisions, exhibit aperiodic oscillations characterized via a mixture of co- and counterrotating oscillations. These aperiodic dynamics qualitatively matched the chaotic motion observed in the numerical model.

A nonlinear analytical formulation for the 1D modelling of a flexible beam in channel flow

The dynamics of flexible beams in confined flows has been a subject of research for many years, as its fundamental behaviour is found in many applications, from energy harvesters to musical instruments. Most studies are concerned solely with the conditions for linear stability and do not explore the ensuing nonlinear behaviour of the system. This is particularly delicate as fluttering beams in confined flows are known to often result in dynamics with intermittent impacts between the beam and the side-walls. Here we present a nonlinear analytical resolution to a simplified 1-D model, based on a modal beam and bulk-flow equations. The model accounts for dissipation through distributed frictional and localized​ head-loss terms. The latter are imposed at the boundary conditions and aim to describe the complex effects occurring outside the domain (turbulence, vortex shedding, etc.). The present analytical resolution leads to a compact system for linear stability analysis, but also to a nonlinear formulation of the fluid–structure interaction. The inclusion of a regularized contact model allows for the computation of the full nonlinear dynamics, including intermittent impacts. Linear stability results are compared to previously published results using 2-D CFD models, and the relative merits of the model are discussed. A variety of limit cycles, (1) with and without impacts, (2) in symmetric and asymmetric configurations and (3) with impacts both at the beam tip and along its length, are shown to illustrate the diversity of dynamics encountered. Moreover, we show that, at large flow velocities, particular model configurations can lead to aperiodic dynamics, a phenomenon reported in several experimental observations. To the authors knowledge, the proposed formulation presents, for the first time, a framework for the comprehensive understanding of the nonlinear dynamics associated with flexible beams in confined axial flow.

Spatiotemporal dynamics of a vortex induced vibration system in the presence of stochastic inflow fluctuations

In this study, influence of stochastic parametric inflow on the spatiotemporal dynamics of a vortex induced vibration system has been examined. The study has been carried out using an incompressible Navier–Stokes based flow solver at a Reynolds number of 100, and it highlights the role of stochastic fluctuations/noise in triggering complex spatiotemporal dynamics in the laminar vortex shedding regime. Wavelets and space–time plots were used to analyse the spatiotemporal data. Noise has been seen to advance the instability regime and alter the frequency characteristics of the response by exciting additional system frequencies, which in turn affects the phase dynamics as well. The study has also revealed that the time scale of the input is an important factor in deciding the dynamics. A short time-scaled noise can trigger aperiodic dynamics, whereas, a long time-scaled input invokes switch states or intermittent states. Noise affects the separation behaviour of the near-field vortices by delaying or advancing it, depending on the regime of operation. For the long time-scaled case, the flow-field becomes a combination of strong or weak von Kárman streets and transitionally disordered wakes. With the short time-scaled noise, the flow-field is predominantly disordered and characterised by phenomena such as vortex pairing and deflected wakes.

Putative rhythms in attentional switching can be explained by aperiodic temporal structure

The neural and perceptual effects of attention were traditionally assumed to be sustained over time, but recent work suggests that covert attention rhythmically switches between objects at 3–8 Hz. Here I use simulations to demonstrate that the analysis approaches commonly used to test for rhythmic oscillations generate false positives in the presence of aperiodic temporal structure. I then propose two alternative analyses that are better able to discriminate between periodic and aperiodic structure in time series. Finally, I apply these alternative analyses to published datasets and find no evidence for behavioural rhythms in attentional switching after accounting for aperiodic temporal structure. The techniques presented here will help clarify the periodic and aperiodic dynamics of perception and of cognition more broadly.

Mapping circuit dynamics during function and dysfunction.

Neural circuits can generate many spike patterns, but only some are functional. The study of how circuits generate and maintain functional dynamics is hindered by a poverty of description of circuit dynamics across functional and dysfunctional states. For example, although the regular oscillation of a central pattern generator is well characterized by its frequency and the phase relationships between its neurons, these metrics are ineffective descriptors of the irregular and aperiodic dynamics that circuits can generate under perturbation or in disease states. By recording the circuit dynamics of the well-studied pyloric circuit in Cancer borealis, we used statistical features of spike times from neurons in the circuit to visualize the spike patterns generated by this circuit under a variety of conditions. This approach captures both the variability of functional rhythms and the diversity of atypical dynamics in a single map. Clusters in the map identify qualitatively different spike patterns hinting at different dynamic states in the circuit. State probability and the statistics of the transitions between states varied with environmental perturbations, removal of descending neuromodulatory inputs, and the addition of exogenous neuromodulators. This analysis reveals strong mechanistically interpretable links between complex changes in the collective behavior of a neural circuit and specific experimental manipulations, and can constrain hypotheses of how circuits generate functional dynamics despite variability in circuit architecture and environmental perturbations.

Spectral Slowing in Chronic Stroke Reflects Abnormalities in Both Periodic and Aperiodic Neural Dynamics

Spectral Slowing in Chronic Stroke Reflects Abnormalities in Both Periodic and Aperiodic Neural Dynamics

Simple and efficient PID algorithm design method for controlling first order systems with a time delay

Many processes in industry are characterized by delay time or by slow aperiodic dynamics called lag behavior. In addition, many plants in the industry are described mathematically by higher order systems that are approximated with the lower order systems, most frequently such processes and systems are described mathematically as first-order-systems-with time-delay (FOSTD), also called first-order-plus-dead-time (FOPDT). The presence of time delays causes degradation and limitation of achieving desired performance, moreover, it can induce instability. In such cases, design of feedback control algorithm becomes difficult and tedious task. The present work suggests an efficient, simple, linear, and easy to apply design expressions for designing continuous PID (proportional-integral-derivative) control algorithm modes to control the behavior of FOPDT systems. The design expressions are intended to overcome negative effects of time delay presence, as well as, to simplify the control algorithm design process and help designer, in easy and simple way, to get system under control with acceptable system stability, medium fastness of response and without or with minimum possible overshoot, oscillation and error. For testing and evaluating the correctness, applicability and efficiency of the derived expressions, MATLAB/Simulink software was applied to develop refined software simulation model that simulates real life values and returns maximum needed numerical and graphical data for assessment process. In addition, various FOSTD systems’ types and forms were used in the simulation model, in particular, systems with small, medium and large time constants, DC gains, and time delay, unstable systems, systems with variable delay. Furthermore, to assess the efficiency of suggested design expressions, the resulted overall system response were compared with resulted responses when two design methods were applied; worldwide known Ziegler Nichols method and MATLAB/Simulink auto-tuned PID block. Analysis of numerical and graphical testing results, show that, The designed control algorithm applying the suggested expressions can, not only simplify the design process, but also, efficient for successful in getting system under control and improving controlling system performance, speeding up response, reduce overshoot, and minimize error, but also stabilize an unstable plants.

Shilnikov chaos, low interest rates, and New Keynesian macroeconomics

The paper shows that in a New Keynesian (NK) model, an active interest rate feedback monetary policy, when combined with a Ricardian passive fiscal policy, à la Leeper-Woodford, may induce the onset of a Shilnikov chaotic attractor in the region of the parameter space where uniqueness of the equilibrium prevails locally. Implications, ranging from long-term unpredictability to global indeterminacy, are discussed in the paper. We find that throughout the attractor, the economy lingers in particular regions, within which the emerging aperiodic dynamics tend to evolve for a long time around lower-than-targeted inflation and nominal interest rates. This can be interpreted as a liquidity trap phenomenon, produced by the existence of a chaotic attractor, and not by the influence of an unintended steady state or the Central Bank's intentional choice of a steady state nominal interest rate at its lower bound. In addition, our finding of Shilnikov chaos can provide an alternative explanation for the controversial “loanable funds” over-saving theory, which seeks to explain why interest rates and, to a lesser extent, inflation rates have declined to current low levels, such that the real rate of interest may be below the marginal product of capital. Paradoxically, an active interest rate feedback policy can cause nominal interest rates, inflation rates, and real interest rates unintentionally to drift downwards within a Shilnikov attractor set. Our results are robust to whether money is in the production function, in the utility function, or not in the model at all. But our results do depend upon the existence of sticky prices.