Rich Dynamics Research Articles

Dressing Avatars

Despite recent progress in developing animatable full-body avatars, realistic modeling of clothing - one of the core aspects of human self-expression - remains an open challenge. State-of-the-art physical simulation methods can generate realistically behaving clothing geometry at interactive rates. Modeling photorealistic appearance, however, usually requires physically-based rendering which is too expensive for interactive applications. On the other hand, data-driven deep appearance models are capable of efficiently producing realistic appearance, but struggle at synthesizing geometry of highly dynamic clothing and handling challenging body-clothing configurations. To this end, we introduce pose-driven avatars with explicit modeling of clothing that exhibit both photorealistic appearance learned from real-world data and realistic clothing dynamics. The key idea is to introduce a neural clothing appearance model that operates on top of explicit geometry: at training time we use high-fidelity tracking, whereas at animation time we rely on physically simulated geometry. Our core contribution is a physically-inspired appearance network, capable of generating photorealistic appearance with view-dependent and dynamic shadowing effects even for unseen body-clothing configurations. We conduct a thorough evaluation of our model and demonstrate diverse animation results on several subjects and different types of clothing. Unlike previous work on photorealistic full-body avatars, our approach can produce much richer dynamics and more realistic deformations even for many examples of loose clothing. We also demonstrate that our formulation naturally allows clothing to be used with avatars of different people while staying fully animatable, thus enabling, for the first time, photorealistic avatars with novel clothing.

Benchmarking the Role of Particle Statistics in Quantum Reservoir Computing

AbstractQuantum reservoir computing is a neuro‐inspired machine learning approach harnessing the rich dynamics of quantum systems to solve temporal tasks. It has gathered attention for its suitability for NISQ devices, for easy and fast trainability, and for potential quantum advantage. Although several types of systems have been proposed as quantum reservoirs, differences arising from particle statistics have not been established yet. In this work, the ability of bosons, fermions, and qubits are assessed and compared to store information from past inputs by measuring linear and nonlinear memory capacity. While, in general, the performance of the system improves with the Hilbert space size, it is shown that also the information spreading capability is a key factor. For the simplest reservoir Hamiltonian choice, and for each boson limited to at most one excitation, fermions provide the best reservoir due to their intrinsic nonlocal properties. On the other hand, a tailored input injection strategy allows the exploitation of the abundance of degrees of freedom of the Hilbert space for bosonic quantum reservoir computing and enhances the computational power compared to both qubits and fermions.

Experimental observation of chaotic hysteresis in Chua's circuit driven by slow voltage forcing

The Chua's circuit has been considered as a paradigm for the investigation of chaos, but it still presents many unexplored dynamics. Chaotic hysteresis is an effect observed when the hysteresis phenomenon and chaotic dynamics phenomenon act simultaneously. It is an interesting phenomenon since it is observed in a variety of disciplines, and it has been utilized in explaining the mechanism of bursting oscillations, rich dynamics in thermal convection, and economic financial crisis, to mention a few. In this paper, we report the experimental observation of chaotic hysteresis in a Chua's electronic circuit driven by both a dc and a slow triangular voltage source. One and two hysteresis loops were observed in single and double scroll chaotic regimes, respectively. We present variations of the attractor that are induced by voltage changes, as well as the dependence of the hysteresis effect on both the driving frequency and the distance from the threshold passing from single to double-scroll chaotic regimes. Our results help in expanding our knowledge on unexplored dynamics of Chua's circuit as well as contribute to chaos control theory with a potential for applications.

Steady and oscillatory flows generated by Eckart streaming in the two-dimensional Rayleigh–Bénard configuration

This paper presents a detailed analysis of the flows induced in a long two-dimensional cavity heated from below in the presence of streaming due to ultrasound acoustic waves emitted by a source. The problem is tackled by using performing spectral element codes, allowing continuation of steady solutions, bifurcation points and periodic cycles. For a given dimensionless source size, the governing parameters are the acoustic streaming parameter $A$ which modulates the acoustic force generating the Eckart streaming and the Rayleigh number ${\textit {Ra}}$ which quantifies the buoyant force responsible for the convection. The streaming flow, which goes to the right along the horizontal axis and returns along the lower and upper boundaries, influences the instability thresholds, which are first strongly stabilized above the pure Rayleigh–Bénard threshold ${\textit {Ra}}_0$ when $A$ is increased, before a destabilization to reach the pure streaming threshold $A_c$ at ${\textit {Ra}}=0$ . The steady multi-roll convective flow generated without streaming is replaced by periodic waves when $A$ is increased, forward waves for moderate $A$ and backward waves for large $A$ . The transition between these waves induces a specific dynamics involving steady flows, which has been elucidated. The waves also eventually disappear for a sufficient increase of the Rayleigh number, replaced by steady multi-roll flows hardly influenced by the streaming flow. A very rich dynamics is thus observed with the competition between the waves and the steady flows.

Soliton dynamics in a piecewise gas-filled hollow-core fiber for efficient dispersive wave emission in the vacuum-ultraviolet range

Table-top coherent vacuum-ultraviolet (VUV) sources are important in many researches. Dispersive wave (DW) emission in a gas-filled hollow-core fiber (HCF) is an efficient way to obtain tunable VUV source with microjoule-level pulse energy. However, the shortest VUV wavelength is limited above 110 nm. This work investigated a method using a piecewise HCF in order to push the shortest VUV DW emission below 110 nm efficiently. The rich and complex spatiotemporal soliton dynamics in the HCF is revealed through rigorous numerical simulations and quantitative analysis. It is found that both the generation of VUV light below 110 nm and the overall conversion efficiencies below 150 nm can be significantly improved if the piecewise gas-filled HCF system is properly designed. As a result, the whole VUV spectrum (200--100 nm) can now be accessed efficiently, with single pulse energy of microjoule level. Different from other widely used intense VUV sources, this source has broad spectrum along with femtosecond time width. These unique characteristics in the VUV spectrum can lead to new research opportunities in various areas.

Diversity and seasonal prevalence of starch hydrolysing, phosphate solubilizing and nitrogen-fixing bacterial groups of rooted and un-rooted regions of tropical mangrove sediments of Sundarbans, West Bengal, India

ABSTRACT The Sundarbans mangrove is a transitional zone between terrestrial land and sea, a unique location in our global geography. This study identifies the richness and population dynamics of bacterial populations along different seasons in the rooted and unrooted regions of soil sediments in Sundarbans, West Bengal. Throughout the year, bacterial populations were higher in the rooted sediment zone, than the unrooted area. The rooted zone contains more silt and clay but the unrooted zone harbours more silty, sandy soil. Salinity is lower in the unrooted zone. The heterotrophic bacterial populations were higher than other types of bacteria in both regions irrespective of seasonal variation. The results revealed that the most varied seasons were the monsoon season in the rooted and unrooted sediment region. The changes identified in this study were most likely due to variances in the microhabitat associated with mangrove root, physicochemical parameters and seasonal fluctuations.

Electronic equivalent of a pump-modulated erbium-doped fiber laser

We built the electronic equivalent circuit based on the model of a pump-modulated erbium-doped fiber laser. The model equations have two state variables, optical field intensity x and population inversion y, and a harmonic modulation applied to the pump parameter. In addition, the model contains two nonlinear terms, xy and ey. The exponential nonlinearity is implemented electronically using a power series expansion. The circuit dynamics is investigated using bifurcation, Lyapunov spectrum, and phase space analyses. Similar to the fiber laser, the equivalent electronic circuit exhibits very rich dynamics, exhibiting chaos and multiple coexisting periodic orbits. The existence of a saddle–node fixed point is demonstrated.

Dynamical mean-field theory: from ecosystems to reaction networks

Both natural ecosystems and biochemical reaction networks involve populations of heterogeneous agents whose cooperative and competitive interactions lead to a rich dynamics of species’ abundances, albeit at vastly different scales. The maintenance of diversity in large ecosystems is a longstanding puzzle, towards which recent progress has been made by the derivation of dynamical mean-field theories of random models. In particular, it has recently been shown that these random models have a chaotic phase in which abundances display wild fluctuations. When modest spatial structure is included, these fluctuations are stabilized and diversity is maintained. If and how these phenomena have parallels in biochemical reaction networks is currently unknown. Making this connection is of interest since life requires cooperation among a large number of molecular species. In this work, we find a reaction network whose large-scale behavior recovers the random Lotka–Volterra model recently considered in theoretical ecology. We clarify the assumptions necessary to derive its large-scale description, and reveal the underlying assumptions made on the noise to recover previous dynamical mean-field theories. Then, we show how local detailed balance and the positivity of reaction rates, which are key physical requirements of chemical reaction networks, provide obstructions towards the construction of an associated dynamical mean-field theory of biochemical reaction networks. Finally, we outline prospects and challenges for the future.

Qualitative analysis and phase of chaos control of the predator-prey model with Holling type-III

In this study, we investigate the dynamics of a discrete-time with predator-prey system with a Holling-III type functional response model. The center manifold theorem and bifurcation theory are used to create existence conditions for flip bifurcations and Neimark-Sacker bifurcations. Bifurcation diagrams, maximum Lyapunov exponents, and phase portraits are examples of numerical simulations that not only show the soundness of theoretical analysis but also show complicated dynamical behaviors and biological processes. From the point of view of biology, this implies that the tiny integral step size can steady the system into locally stable coexistence. Yet, the large integral step size may lead to instability in the system, producing more intricate and richer dynamics. This also means that when the intrinsic death rate of the predator is high, this leads to a chaotic growth rate of the prey. The model has bifurcation features that are similar to those seen in logistic models. In addition, there is a bidirectional Neimark-Sacker bifurcation for both prey and predator, and therefore we obtain a direct correlation in symbiosis. This means that the higher the growth rate of the prey, the greater the growth rate of the predator. Therefore, the operation of predation has increased. The opposite is also true. Finally, the OGY approach is used to control chaos in the predator and prey model. which led to a new concept which we call bifurcation phase of control chaos.

Vibration Analysis of Bistable Unsymmetric Laminates with Curvilinear Fiber Paths

Multistable laminates have been actively studied in recent years due to its potential applications in morphing and energy harvesting devices. Variable stiffness (VS) bistable laminates provide opportunities for further improvements in design space in comparison with constant stiffness bistable laminates. The snap-through process involving shape transition between the stable configurations is highly nonlinear in nature and exhibits rich dynamics. Exploiting the dynamic characteristics during the snap-through transition is of considerable interest in designing the morphing structural components. In this paper, we present a semi-analytical model based on Rayleigh–Ritz approach in conjunction with Hamilton’s principle to predict the natural frequencies of bistable VS laminates. The obtained results are compared with the results from the full geometrically nonlinear finite element (FE) model. The proposed FE model is further extended to study the dynamics of VS laminates subjected to external forces with different amplitudes. Subsequently, a parametric study is performed to explore the effect of different curvilinear fiber alignments on natural frequencies, mode shapes, free vibration characteristics and forced vibration characteristics (single-well and cross-well vibrations).

Noisy quantum kernel machines

In the noisy intermediate-scale quantum era, an important goal is the conception of implementable algorithms that exploit the rich dynamics of quantum systems and the high dimensionality of the underlying Hilbert spaces to perform tasks while prescinding from noise-proof physical systems. An emerging class of quantum learning machines is that based on the paradigm of quantum kernels. Here, we study how dissipation and decoherence affect their performance. We address this issue by investigating the expressivity and the generalization capacity of these models within the framework of kernel theory. We introduce and study the effective kernel rank, a figure of merit that quantifies the number of independent features a noisy quantum kernel is able to extract from input data. Moreover, we derive an upper bound on the generalization error of the model that involves the average purity of the encoded states. Thereby we show that decoherence and dissipation can be seen as an implicit regularization for the quantum kernel machines. As an illustrative example, we report exact finite-size simulations of machines based on chains of driven-dissipative quantum spins to perform a classification task, where the input data are encoded into the driving fields and the quantum physical system is fixed. We determine how the performance of noisy kernel machines scales with the number of nodes (chain sites) as a function of decoherence and examine the effect of imperfect measurements.

Logics in Fungal Mycelium Networks

The living mycelium networks are capable of efficient sensorial fusion over very large areas and distributed decision making. The information processing in the mycelium networks is implemented via propagation of electrical and chemical signals en pair with morphological changes in the mycelium structure. These information processing mechanisms are manifested in experimental laboratory findings that show that the mycelium networks exhibit rich dynamics of neuron-like spiking behaviour and a wide range of non-linear electrical properties. On an example of a single real colony of Aspergillus niger, we demonstrate that the non-linear transformation of electrical signals and trains of extracellular voltage spikes can be used to implement logical gates and circuits. The approaches adopted include numerical modelling of excitation propagation on the mycelium network, representation of the mycelium network as a resistive and capacitive network and an experimental laboratory study on mining logical circuits in mycelium bound composites.

Attractors and long transients in a spatio-temporal slow–fast Bazykin’s model

Spatio-temporal complexity of ecological dynamics has been a major focus of research for a few decades. Pattern formation, chaos, regime shifts and long transients are frequently observed in field data but specific factors and mechanisms responsible for the complex dynamics often remain obscure. An elementary building block of ecological population dynamics is a prey–predator system. In spite of its apparent simplicity, it has been demonstrated that a considerable part of ecological dynamical complexity may originate in this elementary system. A significant progress in understanding of the prey–predator system’s potential complexity has been made over the last few years; however, there are yet many questions remaining. In this paper, we focus on the effect of intraspecific competition in the predator population; the prey–predator model accounting for such competition is known as Bazykin’s model. We pay a particular attention to the case (often observed in real population communities) where the inherent prey and predator timescales are significantly different: the property known as a ‘slow–fast’ dynamics. Using an array of analytical methods along with numerical simulations, we provide a detailed analysis for the existence of Turing bifurcation and corresponding Turing pattern. We show how the Turing domain and corresponding spatial pattern changes in the presence of different (slow–fast) timescales. In doing that, we apply a novel approach to quantify the system solution by calculating its norm in two different metrics such as C0 and L2. We show that the slow–fast Bazykin’s system exhibits a rich spatio-temporal dynamics, including a variety of long transient regimes that can last for hundreds and thousands of generations.

Evolution of cooperation in multigame with environmental space and delay

Replicator dynamics is widely used in evolutionary game theory, however, most previous studies on replicator dynamics focus on single games and ignore multiple social dilemmas encountered by individuals in a population. This paper uses replicator dynamics to construct a multigame system with environmental space and delay based on three social dilemmas. For the non-delayed and delayed multigame systems, rich dynamics for stability, bistability, transcritical bifurcation, Hopf bifurcation, and the direction, stability and periodic variation of periodic solutions are comprehensively investigated. Accordingly, we use numerical simulations to assist in exploring the effects of multigame, environmental space, and time delay on strategic dynamics. The results show that large proportions of snowdrift game and stag hunt game are conducive to the prosperity of cooperators, and defectors are easy to survive when the proportion of prisoner’s dilemma is large. The cooperator gains the advantage of benefit distribution from environmental space, or the defector gets less benefit distribution as punishment, which will make pure cooperation the dominant strategy. Furthermore, environmental space can allow cooperation and defection to coexist oscillatingly. Interestingly, large delays reverse the coexistence of cooperation and defection to a situation dominated by the purely cooperative strategy.

Nonlinear dynamic modeling of bistable variable stiffness composite laminates

The room-temperature equilibrium stable states of cured unsymmetric composite laminates have been the focus of recent research, with a particular emphasis on shape morphing applications. It has been shown that changing the fiber orientation of unsymmetrical laminates using curvilinear fiber path description can results in a plethora of bistable configurations with an enriched design space. In bistable structures, snap-through involves transition from one stable shape to another, which is a non-linear phenomenon exhibiting rich dynamics during the shape transition. Past works involving such dynamic characteristics show encouraging potential in designing efficient morphing strategies. In this work, a novel semi-analytical model using Föppl von Kármán kinematics has been formulated to predict the non-linear dynamic characteristic of bistable variable stiffness (VS) laminates. An efficient energy formulation is adopted where the membrane and bending energies are decoupled using the semi-inverse constitutive equation. The in-plane stress resultants and the energy components are expressed in terms of curvatures using the in-plane equilibrium equations and compatibility conditions. Using Hamilton’s principle in conjunction with the Rayleigh–Ritz approach, a set of non-linear equations are generated, which is solved to obtain the dynamics of the snap-through process. The accuracy of the predicted non-linear vibration results of bistable plates from the semi-analytical model is verified using a fully non-linear finite element framework and validated exemplarily by tests on a straight fiber laminate configuration. Finally, a parametric study is performed by tailoring the VS parameters to identify the effect of different curvilinear fiber alignments on the dynamic characteristics of bistable VS laminates.

Abstract 14927: Real-Time Super-Resolution Analysis of Sarcomere Motion Reveals Context-Dependent Stochastic Heterogeneity in Induced Pluripotent Stem Cell-Derived Cardiomyocytes

Studies of sarcomere dynamics in cardiac myofibrils are key to understand how myosin-actin contractility translates to whole heart contractions. Such analyses require high spatial (nm) and temporal (ms) resolution of multiple sarcomeres in parallel. Here, we present a new imaging and computational method to analyze sarcomere structure and function in human induced pluripotent stem cell (iPSC)-derived cardiomyocytes. For this we (1) engineered a fluorescent z-band tag (ACTN2-Citrine) by CRISPR-editing, (2) developed micropatterned soft (7:1, 10 kPa) substrate cultures to mimic in vivo conditions, (3) made use of high-speed microscopy (66 fps), and (4) designed an automated AI-based sarcomere detection and analysis tool (SarcAsM - Sarcomere Analysis Multitool). Cardiomyocytes were differentiated from the ACTN2-Citrine iPSC-line and purified using a staged growth factor and metabolic selection protocol (>95% purity with a ventricular myocyte phenotype). Our analysis revealed highly heterogeneous single sarcomere motion, i.e., shortening and lengthening patterns during the same time of the contraction cycle. Notably, the observed rich dynamics on single sarcomere-level are not apparent from whole cell analyses. Interestingly, culture on stiffer substrates (>20 kPa; mimicking cardiac fibrosis) resulted in reduced cell-level contraction, but constant sarcomere level contractility with however enhanced heterogeneity. Analysis of a large data set (>1,200 cells) in conjunction with a biophysical model showed that heterogeneous sarcomere motion is not caused by static non-uniformity (e.g., strong/weak sarcomeres), but can be primarily attributed to the stochastic and non-linear nature of sarcomere dynamics and thus occurs intrinsically during cardiomyocyte beating. Our findings show that that sarcomere heterogeneity is an important feature of cardiomyocyte contractility. The introduced tools for unbiased high-throughput analysis of sarcomere-level dynamics can be exploited to gain a better understanding on how sarcomere level contractility translates to whole cardiomyocyte contractions under simulated physiological and pathological conditions.

Enhancement of synchronization bandwidth in an arch beam

Synchronization in microstructures has been widely investigated because of its rich dynamics and promising applications. Most investigations are devoted to revealing the basic features or enhancing the application performance in oscillator with hardening nonlinearity. However, few theoretical and experimental studies have been conducted on synchronization with softening nonlinearity, which easily occurs in imperfect manufacturing. In this paper, we built up a phase feedback loop with an arch beam that exhibits softening effect subjected to a synchronization perturbation. Theoretical analysis and experimental verification are applied to explore the effects of the feedback phase delay and nonlinearity on the synchronization bandwidth. The optimal phase delay for best synchronization bandwidth is determined and the significant enhancement of nonlinearity on the synchronization bandwidth is observed. An practical approach of manipulating the nonlinearity strength is proposed by tuning the ratio of the applied ac voltage VAC to DC voltage VDC. The presented foundings provide novel strategies to enhance the synchronization bandwidth in nonlinear oscillator with softening effects.

Four-dimensional Hindmarsh–Rose neuron model with hidden firing multistability based on two memristors

Since memristors can be used to describe electromagnetic induction effects, this paper proposes a novel 4D HindMarsh-Rose (HR) neuron model based on two flux-controlled memristors to show complex dynamics of neuronal electrical activity. It has no equilibrium point, revealing hidden dynamical behaviors. The complex dynamics of the system are illustrated by phase portraits, the time sequences, bifurcation diagrams, and Lyapunov exponents spectra. The presented 4D HR neuron model can produce coexisting multiple hidden firing patterns, for instance, periodic spiking, chaotic spiking, transient chaotic spiking, periodic bursting, chaotic bursting, transient chaotic bursting, stochastic bursting, and transient stochastic bursting. Besides, rich nonlinear dynamics, such as anti-monotonicity and initial offset boosting, are also found. Finally, Multisim circuit simulation is performed and the results are in accordance with numerical simulation.

Spatially inhomogeneous periodic patterns induced by distributed memory in the memory-based single population model

In this paper, we investigate the influence of the distributed delay on the stability and spatiotemporal dynamics in the memory-based diffusion single population model. Under the assumption that the positive equilibrium of the corresponding ordinary differential equation is locally asymptotically stable, it has been shown that the weak kernel does not affect the stability of this positive constant steady state, but for the strong kernel, the combined effect of the diffusion rate of the memory diffusion and the distributed delay can affect the stability and lead to the rich dynamics. For the strong kernel, the theoretical conditions for the stability, Hopf bifurcation and double Hopf bifurcation are explicitly determined.

Rich complex dynamics in new fractional-order hyperchaotic systems using a modified Caputo operator based on the extended Gamma function

In this work, rich complex dynamics are observed in new fractional-order hyperchaotic systems when employing a modified Caputo-operator based on the extended Gamma function. Thus, the new parameter of the extended Gamma function provides higher degree of freedom that plays a vital role in the appearance (or disappearance) of chaotic attractors. Two numerical examples are provided to validate the proposed method. The numerical examples show that various chaotic, hyperchaotic and non-chaotic attractors are obtained when varying the new parameter of the modified Caputo-operator.In conclusion, this work shows that the modified Caputo-operator possesses higher degree of freedom than the classic one. This interesting phenomena result in obtaining rich complex dynamics in the systems that involve this new operator including phase transition from hyperchaotic to chaotic states and also phase transition from chaotic to non-chaotic states. Moreover, we show in the second numerical example that chaotic attractors exist only with the modified Caputo-operator using a specific choice of the system’s parameters, while the system’s counterpart does not show chaotic behaviors when using the classic Caputo-operator. Thus, the fractional systems with the modified Caputo-operator are shown to exhibit stronger chaotic dynamics than their counterparts with the old (classic) Caputo-operator.