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An extended FitzHugh–Nagumo model is developed to model the synaptic coupling of neurons and the associated dynamics. The neurons are coupled via chemical synapses, which can excite or inhibit the postsynaptic neuron. The neurotransmitter-receptor dynamics is governed with a gating dynamic, which allows for the distinction between fast and slow synapses. Detailed nonlinear dynamics analysis are performed for simple neural motifs of a self-synapsed neuron and two synaptically coupled neurons for the instabilities that lead to neural oscillations, and the associated phase diagrams are obtained. Interesting dynamics such as synchronization of fast and slow firing neurons, frequency enhancement, quiescent neurons coupled to oscillators, chaotic spiking, and periodic bursting are found.

We report a systematic study of the dynamics of self-propelled particles (SPPs) over a one-dimensional periodic potential landscape, which is fabricated on a microgroove-patterned polydimethylsiloxane (PDMS) substrate. From the measured non-equilibrium probability density function of the SPPs, we find that the escape dynamics of the slow-rotating SPPs across the potential landscape can be described by an effective potential, once the self-propulsion force is included into the potential under the fixed angle approximation. This work demonstrates that the parallel microgrooves provide a versatile platform for a quantitative understanding of the interplay among the self-propulsion force, spatial confinement by the potential landscape, and thermal noise, as well as its effects on activity-assisted escape dynamics and transport of the SPPs.

We experimentally demonstrate that a Brownian gyrator of a colloidal particle confined in a two-dimensional harmonic potential with different effective temperatures on orthogonal axes can work as an autonomous heat engine capable of extracting work from the heat bath, generated by an optical feedback trap. The results confirm the theoretically predicted thermodynamic currents and validate the attainability of Carnot efficiency as well as the trade-off relation between power and efficiency. We further show that current fluctuations and the entropy production rate are time independent in the steady state and their product near the Carnot efficiency is close to the lower bound of the thermodynamic uncertainty relation.

We consider coupled network dynamics under uncorrelated noises that fluctuate about the noise-free long-time asymptotic state. Our goal is to reconstruct the directed network only from the time-series data of the dynamics of the nodes. By using the stochastic force inference method with a simple natural choice of linear polynomial basis, we derive a reconstruction scheme of the connection weights and the noise strength of each node. Explicit simulations for directed and undirected random networks with various node dynamics are carried out to demonstrate the good accuracy and high efficiency of the reconstruction scheme. We further consider the case when only a subset of the network and its node dynamics can be observed, and it is demonstrated that the directed weighted connections among the observed nodes can be easily and faithfully reconstructed. In addition, we propose a scheme to infer the number of hidden nodes and their effects on each observed node. The accuracy of these results is illustrated by simulations.

In the study of biological networks, one of the major challenges is to understand the relationships between network structure and dynamics. In this paper, we model in vitro cortical neuronal cultures as stochastic dynamical systems and apply a method that reconstructs directed networks from dynamics [Ching and Tam, Phys. Rev. E 95, 010301(R) (2017)2470-004510.1103/PhysRevE.95.010301] to reveal directed effective connectivity, namely, the directed links and synaptic weights, of the neuronal cultures from voltage measurements recorded by a multielectrode array. The effective connectivity so obtained reproduces several features of cortical regions in rats and monkeys and has similar network properties as the synaptic network of the nematode Caenorhabditis elegans, whose entire nervous system has been mapped out. The distribution of the incoming degree is bimodal and the distributions of the average incoming and outgoing synaptic strength are non-Gaussian with long tails. The effective connectivity captures different information from the commonly studied functional connectivity, estimated using statistical correlation between spiking activities. The average synaptic strengths of excitatory incoming and outgoing links are found to increase with the spiking activity in the estimated effective connectivity but not in the functional connectivity estimated using the same sets of voltage measurements. These results thus demonstrate that the reconstructed effective connectivity can capture the general properties of synaptic connections and better reveal relationships between network structure and dynamics.

Identifying the mechanism of intercellular feedback regulation is critical for the basic understanding of tissue growth control in organisms. In this paper, we analyze a tissue growth model consisting of a single lineage of two cell types regulated by negative feedback signalling molecules that undergo spatial diffusion. By deriving the fixed points for the uniform steady states and carrying out linear stability analysis, phase diagrams are obtained analytically for arbitrary parameters of the model. Two different generic growth modes are found: blow-up growth and final-state controlled growth which are governed by the non-trivial fixed point and the trivial fixed point respectively, and can be sensitively switched by varying the negative feedback regulation on the proliferation of the stem cells. Analytic expressions for the characteristic time scales for these two growth modes are also derived. Remarkably, the trivial and non-trivial uniform steady states can coexist and a sharp transition occurs in the bistable regime as the relevant parameters are varied. Furthermore, the bi-stable growth properties allows for the external control to switch between these two growth modes. In addition, the condition for an early accelerated growth followed by a retarded growth can be derived. These analytical results are further verified by numerical simulations and provide insights on the growth behavior of the tissue. Our results are also discussed in the light of possible realistic biological experiments and tissue growth control strategy. Furthermore, by external feedback control of the concentration of regulatory molecules, it is possible to achieve a desired growth mode, as demonstrated with an analysis of boosted growth, catch-up growth and the design for the target of a linear growth dynamic., Comment: to be published in Physical Review E

Ehrenfest urns with interaction that are connected in a ring is considered as a paradigm model for non-equilibrium thermodynamics and is shown to exhibit two distinct non-equilibrium steady states (NESS) of uniform and non-uniform particle distributions. As the inter-particle attraction varies, a first order non-equilibrium phase transition occurs between these two NESSs characterized by a coexistence regime. The phase boundaries, the NESS particle distributions near saddle points and the associated particle fluxes, average urn population fractions, and the relaxational dynamics to the NESSs are obtained analytically and verified numerically. A generalized non-equilibrium thermodynamics law is also obtained, which explicitly identifies the heat, work, energy and entropy of the system., 12 pages, 12 figures

We consider a quasi two-dimensional network connection growth model that minimizes the wiring cost while maximizing the network connections, but at the same time edge crossings are penalized or forbidden. This model is mapped to a dilute anti-ferromagnetic Ising spin system with frustrations. We obtain analytic results for the order-parameter or mean degree of the optimized network using mean field theories. The cost landscape is analyzed in detail showing complex structures due to frustration as the crossing penalty increases. For the case of strictly no edge crossing is allowed, the mean-field equations lead to a new algorithm that can effectively find the (near) optimal solution even for this strongly frustrated system. All these results are also verified by Monte Carlo simulations and numerical solution of the mean-field equations. Possible applications and relation to the planar triangulation problem is also discussed.

We consider coupled network dynamics under uncorrelated noises, but only a subset of the network and their node dynamics can be observed. The effects of hidden nodes on the dynamics of the observed nodes can be viewed as having an extra effective noise acting on the observed nodes. These effective noises possess spatial and temporal correlations whose properties are related to the hidden connections. The spatial and temporal correlations of these effective noises are analyzed analytically and the results are verified by simulations on undirected and directed weighted random networks and small-world networks. Furthermore, by exploiting the network reconstruction relation for the observed network noisy dynamics, we propose a scheme to infer information of the effects of the hidden nodes such as the total number of hidden nodes and the weighted total hidden connections on each observed node. The accuracy of these results are demonstrated by explicit simulations.

We study the nonequilibrium steady-state (NESS) dynamics of two-dimensional Brownian gyrators under harmonic and nonharmonic potentials via computer simulations and analyses based on the Fokker-Planck equation, while our nonharmonic cases feature a double-well potential and an isotropic quartic potential. In particular, we report two simple methods that can help understand gyrating patterns. For harmonic potentials, we use the Fokker-Planck equation to survey the NESS dynamical characteristics, i.e., the NESS currents gyrate along the equiprobability contours and the stationary point of flow coincides with the potential minimum. As a contrast, the NESS results in our nonharmonic potentials show that these properties are largely absent, as the gyrating patterns are much distinct from those of corresponding probability distributions. Furthermore, we observe a critical case of the double-well potential, where the harmonic contribution to the gyrating pattern becomes absent, and the NESS currents do not circulate about the equiprobability contours nearby the potential minima even at low temperatures., 9 pages, 3 figures

Electric circuits influenced by thermal noise are analogous to confined Brownian particles and can be an alternative and convenient scheme for studying stochastic thermodynamics. Here we experimentally demonstrate an effective technique of generating tunable potentials for Brownian dynamics in an electric circuit, realized by external controlled feedback. We present two illustrative examples of one-dimensional virtual potentials: static harmonic potential and time-varying double-well potential. The thermal noises of both cases undergo equivalent Brownian dynamics as if they were in the authentic potentials as long as the feedback is fast enough to respond to the designed potentials. The results show that the electric circuit provides a simple, effective, and programmable scheme to study the feedback-controlled virtual potential.

Studying connectivity of neuronal cultures can provide insights for understanding brain networks but it is challenging to reveal neuronal connectivity from measurements. We apply a novel method that uses a theoretical relation between the time-lagged cross-covariance and the equal-time cross-covariance to reveal directed effective connectivity and synaptic weights of cortical neuron cultures at different days in vitro from multielectrode array recordings. Using a stochastic leaky-integrate-and-fire model, we show that the simulated spiking activity of the reconstructed networks can well capture the measured network bursts. The neuronal networks are found to be highly nonrandom with an over-representation of bidirectionally connections as compared to a random network of the same connection probability, with the fraction of inhibitory nodes comparable to the measured fractions of inhibitory neurons in various cortical regions in monkey, and have small-world topology with basic network measures comparable to those of the nematode C. elegans chemical synaptic network. Our analyses further reveal that (i) the excitatory and inhibitory incoming degrees have bimodal distributions the excitatory and inhibitory incoming degrees have bimodal distributions, which are that distributions that have been indicated to be optimal against both random failures and attacks in undirected networks; (ii) the distribution of the physical length of excitatory incoming links has two peaks indicating that excitatory signal is transmitted at two spatial scales, one localized to nearest nodes and the other spatially extended to nodes millimeters away, and the shortest links are mostly excitatory towards excitatory nodes and have larger synaptic weights on average; (iii) the average incoming and outgoing synaptic strength is non-Gaussian with long tails and, in particular, the distribution of outgoing synaptic strength of excitatory nodes with excitatory incoming synaptic strength is lognormal, similar to the measured excitatory postsynaptic potential in rat cortex.Author summaryTo understand how the brain processes signal and carries out its function, it is useful to know the connectivity of the underlying neuronal circuits. For large-scale neuronal networks, it is difficult to measure connectivity directly using electron microscopy techniques and methods that can estimate connectivity from electrophysiological recordings are thus highly desirable. Existing methods focus mainly on estimating functional connectivity, which is defined by statistical dependencies between neuronal activities but the relevant direct casual interactions are captured by effective connectivity. Here we apply a novel covariance-relation based method to estimate the directed effective connectivity and synaptic weights of cortical neuron cultures from recordings of multielectrode array of over 4000 electrodes taken at different days in vitro. The neuronal networks are found to be nonrandom, small-world, excitation/inhibition balanced as measured in monkey cortex, and with feeder hubs. Our analyses further suggest some form of specialisation of nodes in receiving excitatory and inhibitory signals and the transmission of excitatory signals at two spatial scales, one localized to nearest nodes and the other spatially extended to nodes millimeters away, and reveal that the distributions of the average incoming and outgoing synaptic strength are skewed with long tails.

A model based on the classic non-interacting Ehrenfest urn model with two-urns is generalized to $M$ urns with the introduction of interactions for particles within the same urn. As the inter-particle interaction strength is varied, phases of different levels of non-uniformity emerge and their stabilities are calculated analytically. In particular, coexistence of locally stable uniform and non-uniform phases connected by first-order transition occurs. The phase transition threshold and energy barrier can be derived exactly together with the phase diagram obtained analytically. These analytic results are further confirmed by Monte Carlo simulations., 23 pages, 7 figures

Reconstructing the structure of complex networks from measurements of the nodes is a challenge in many branches of science. External influences are always present and act as a noise to the networks of interest. In this paper, we present a method for reconstructing networks from measured dynamics of the nodes subjected to correlated noise that cannot be approximated by a white noise. This method can reconstruct the links of both bidirectional and directed networks, the correlation time and strength of the noise, and also the relative coupling strength of the links when the coupling functions have certain properties. Our method is built upon theoretical relations between network structure and measurable quantities from the dynamics that we have derived for systems that have fixed point dynamics in the noise-free limit. Using these theoretical results, we can further explain the shortcomings of two common practices of inferring links for bidirectional networks using the Pearson correlation coefficient and the partial correlation coefficient.

A two-layer colloidal system is developed for the study of diffusion over a quenched two-dimensional random potential. A mixture of bidisperse silica spheres is used to form a randomly packed colloidal monolayer on the bottom substrate. The corrugated surface of the bottom colloidal monolayer provides a gravitational potential field for the dilute diffusing particles in the top layer. The population probability histogram P(x,y) of the diffusing particles is obtained to fully characterize the random potential landscape U(x,y) via the Boltzmann distribution. The dynamical properties of the top diffusing particles, such as their mean square displacement (MSD), histogram of the escape time, and long-time self-diffusion coefficient, are simultaneously measured from the particle trajectories. A quantitative relationship between the long-time diffusion coefficient and the random potential is obtained, which is in good agreement with the theoretical prediction. The measured MSD reveals a wide region of subdiffusion resulting from the structural disorders. The crossover from subdiffusion to normal diffusion is explained by the Lorentz model for tracer diffusion through a heterogeneous space filled with a set of randomly distributed obstacles.

We formulate and analyze oscillatory dynamics associated with a model of dynamically active, but spatially segregated, compartments that are coupled through a chemical signal that diffuses in the bulk medium between the compartments. The coupling between each compartment and the bulk is due to both feedback terms to the compartmental dynamics and flux boundary conditions at the interface between the compartment and the bulk. Our coupled model consists of dynamically active compartments located at the two ends of a 1-D bulk region of spatial extent 2 L . The dynamics in the two compartments is modeled by Sel’kov kinetics, and the signaling molecule between the two-compartments is assumed to undergo both diffusion, with diffusivity D , and first-order, linear, bulk degradation. For the resulting PDE–ODE system, we construct a symmetric steady-state solution and analyze the stability of this solution to either in-phase synchronous or anti-phase synchronous perturbations about the midline x = L . The conditions for the onset of oscillatory dynamics, as obtained from a linearization of the steady-state solution, are studied using a winding number approach. Global branches of either in-phase or anti-phase periodic solutions, and their associated stability properties, are determined numerically. For the case of a linear coupling between the compartments and the bulk, with coupling strength β , a phase diagram, in the parameter space D versus β is constructed that shows the existence of a rather wide parameter regime where stable in-phase synchronized oscillations can occur between the two compartments. By using a Floquet-based approach, this analysis with linear coupling is then extended to determine Hopf bifurcation thresholds for a periodic chain of evenly-spaced dynamically active units. Finally, we consider one particular case of a nonlinear coupling between two active compartments and the bulk. It is shown that stable in-phase and anti-phase synchronous oscillations also occur in certain parameter regimes, but as isolated solution branches that are disconnected from the steady-state solution branch.

We employ the sorted local transfer entropy (SLTE) to reconstruct the coupling strengths of Ising spin networks with positive and negative couplings (J_{ij}), using only the time-series data of the spins. The SLTE method is model-free in the sense that no knowledge of the underlying dynamics of the spin system is required and is applicable to a broad class of systems. Contrary to the inference of coupling from pairwise transfer entropy, our method can reliably distinguish spin pair interactions with positive and negative couplings. The method is tested for the inverse Ising problem for different J_{ij} distributions and various spin dynamics, including synchronous and asynchronous update Glauber dynamics and Kawasaki exchange dynamics. It is found that the pairwise SLTE is proportional to the pairwise coupling strength to a good extent for all cases studied. In addition, the reconstruction works well for both the equilibrium and nonequilibrium cases of the time-series data. Comparison to other inverse Ising problem approaches using mean-field equations is also discussed.

Effects of mechanical coupling on cardiac dynamics are studied by monitoring the beating dynamics of a cardiac tissue which is being pulled periodically at a pace slower than its intrinsic beating rate. The tissue is taken from the heart of a bullfrog that includes pacemaker cells. The cardiac tissue beats spontaneously with an almost constant interbeat interval (IBI) when there is no external forcing. On the other hand, the IBI is observed to vary significantly under an external periodic drive. Interestingly, when the period of the external drive is about two times the intrinsic IBI of the tissue without pulling, the IBI as a function of time exhibits a wave packet structure. Our experimental results can be understood theoretically by a phase-coupled model under external driving. In particular, the theoretical prediction of the wave-packet period as a function of the normalized driving period agrees excellently with the observations. Furthermore, the cardiac mechanical coupling constant can be extracted from the experimental data from our model and is found to be insensitive to the external driving period. Implications of our results on cardiac physiology are also discussed.

Realizing quasistatic processes in finite times requires additional control parameters to keep the system in instantaneous equilibrium (ieq). However, the finite-rate ieq transition of the reverse process is not just the time-reversal of the ieq forward process due to the odd-parity of controlling parameters. We theoretically show a work relation that the dissipated work of the ieq transition of the forward process is the same as that of the corresponding reverse process. The work relation can be interpreted as a generalization of equilibrium (quasistatic) processes. The work relation and the associated statistics of nonequilibrium work are experimentally confirmed in three different Brownian systems: the time-varying harmonic and non-harmonic potentials and the Brownian harmonic transport, which are manipulated by the optical feedback trap.

We experimentally realize the finite-rate isothermal process of a Brownian particle in a breathing harmonic potential. For the compression process, finite-rate equilibration can be achieved by increasing and then decreasing the stiffness of the potential to the final stiffness according to the shortcuts-to-isothermal (ScI) protocol. On the other hand, the realization of the ScI expansion is experimentally impossible with optical tweezers due to the requirement of a negative stiffness. Here, we propose a simple and elegant method to resolve this problem and demonstrate the ScI expansion by using the optical feedback trap capable of creating an arbitrary spatiotemporal potential even with a negative stiffness. In addition, we check the thermodynamic energetics such as work, heat, and internal energy, which indeed obey stochastic thermodynamics. Our method provides the possibility of a Brownian heat engine with maximum efficiency but non-vanishing power.

Rare massive eruption of thermal plumes causes random reversals of the large-scale flow in turbulent thermal convection., It is commonly believed that heat flux passing through a closed thermal convection system is balanced so that the convection system can remain at a steady state. Here, we report a new kind of convective instability for turbulent thermal convection, in which the convective flow stays over a long steady “quiet period” having a minute amount of heat accumulation in the convection cell, followed by a short and intermittent “active period” with a massive eruption of thermal plumes to release the accumulated heat. The rare massive eruption of thermal plumes disrupts the existing large-scale circulation across the cell and resets its rotational direction. A careful analysis reveals that the distribution of the plume eruption amplitude follows the generalized extreme value statistics with an upper bound, which changes with the fluid properties of the convecting medium. The experimental findings have important implications to many closed convection systems of geophysical scale, in which massive eruptions and sudden changes in large-scale flow pattern are often observed.

The nonlinear dynamical properties of the recently proposed [Formula: see text] feedback control for suppressing cardiac alternans is investigated in detail for the discrete cardiac restitution map model and the continuous Luo–Rudy I ionic model. It is shown that cardiac alternans, induced by fast pacing, can be dramatically reduced by small changes of fixed magnitude ([Formula: see text]) under feedback control when [Formula: see text] exceeds a critical threshold. Remarkably, the suppression is achieved by utilizing the induced chaotic dynamics. Detailed information on the nature and mechanism of the control, and properties of the attractors are analyzed and discussed in the light of nonlinear dynamics.

The population dynamics of two interacting species modeled by the Lotka-Volterra (LV) model with general parameters that can promote or suppress the other species is studied. It is found that the properties of the two species' isoclines determine the interaction of species, leading to six regimes in the phase diagram of interspecies interaction; i.e., there are six different interspecific relationships described by the LV model. Four regimes allow for nontrivial species coexistence, among which it is found that three of them are stable, namely, weak competition, mutualism, and predator-prey scenarios can lead to win-win coexistence situations. The Lyapunov function for general nontrivial two-species coexistence is also constructed. Furthermore, in the presence of spatial diffusion of the species, the dynamics can lead to steady wavefront propagation and can alter the population map. Propagating wavefront solutions in one dimension are investigated analytically and by numerical solutions. The steady wavefront speeds are obtained analytically via nonlinear dynamics analysis and verified by numerical solutions. In addition to the inter- and intraspecific interaction parameters, the intrinsic speed parameters of each species play a decisive role in species populations and wave properties. In some regimes, both species can copropagate with the same wave speeds in a finite range of parameters. Our results are further discussed in the light of possible biological relevance and ecological implications.

A tilted two-layer colloidal system is constructed for the study of force-assisted barrier-crossing dynamics over a periodic potential. The periodic potential is provided by the bottom layer colloidal spheres forming a fixed crystalline pattern on a glass substrate. The corrugated surface of the bottom colloidal crystal provides a gravitational potential field for the top layer diffusing particles. By tilting the sample at an angle θ with respect to the vertical (gravity) direction, a tangential component of the gravitational force F is applied to the diffusing particles. The measured mean drift velocity v(F, Eb) and diffusion coefficient D(F, Eb) of the particles as a function of F and energy barrier height Eb agree well with the exact results of the one-dimensional drift velocity (R. L. Stratonovich, Radiotekh. Elektron, 1958, 3, 497) and diffusion coefficient (P. Reimann, et al., Phys. Rev. Lett., 2001, 87, 010602 and P. Reimann, et al., Phys. Rev. E, 2002, 65, 031104). Based on these exact results, we show analytically and verify experimentally that there exists a scaling region, in which v(F, Eb) and D(F, Eb) both scale as ν′(F)exp[−E*b(F)/kBT], where the Arrhenius pre-factor ν′(F) and effective barrier height E*b(F) are both modified by F. The experiment demonstrates the applications of this model system in evaluating different scaling forms of ν′(F) and E*b(F) and their accuracy, in order to extract useful information about the external potential, such as the intrinsic barrier height Eb.

Cardiac alternans may lead to life-threatening arrhythmias or sudden cardiac death. Thus, finding an effective method to suppress alternans is crucial. In this paper, we demonstrate that the time needed to control cardiac alternans induced by rapid pacing using the T+T-feedback control can be dramatically shortened if the extracellular calcium concentration is lowered by a very small amount when the control is turned on. Numerical simulations are performed on the Hund-Rudy dynamic (HRd) model for single cell. Since controlling alternans is important as it can be a precursor of sudden cardiac death, the results of our research may have important clinical implications and will lead to the development of a better control scheme for alternans or a smart defibrillator.

We report a systematic study of the forward and reverse transition probability density functions (TPDFs) and entropy production in a nonequilibrium steady state (NESS). The NESS is realized in a two-layer colloidal system, in which the bottom-layer colloidal crystal provides a two-dimensional periodic potential U_{0}(x,y) for the top-layer diffusing particles. By tilting the sample at an angle with respect to gravity, a tangential component of the gravitational force F is applied to the diffusing particles, which breaks the detailed balance (DB) condition and generates a steady particle flux along the [1,0] crystalline orientation. While both the measured forward and reverse TPDFs reveal interesting space-time dependence, their ratio is found to be independent of time and obeys a DB-like relation. The experimental results are in good agreement with the theoretical predictions. This study thus provides a better understanding on how entropy is generated and heat is dissipated to the reservoir during a NESS transition process. It also demonstrates the applications of the two-layer colloidal system in the study of NESS transition dynamics.

Reconstructing network connection topology and interaction strengths solely from measurement of the dynamics of the nodes is a challenging inverse problem of broad applicability in various areas of science and engineering. For a discrete-time step network under noises whose noise-free dynamics is stationary, we derive general analytic results relating the weighted connection matrix of the network to the correlation functions obtained from time-series measurements of the nodes for networks with one-dimensional intrinsic node dynamics. Information about the intrinsic node dynamics and the noise strengths acting on the nodes can also be obtained. Based on these results, we develop a scheme that can reconstruct the above information of the network using only the time-series measurements of node dynamics as input. Reconstruction formulas for higher-dimensional node dynamics are also derived and illustrated with a two-dimensional node dynamics network system. Furthermore, we extend our results and obtain a reconstruction scheme even for the cases when the noise-free dynamics is periodic. We demonstrate that our method can give accurate reconstruction results for weighted directed networks with linear or nonlinear node dynamics of various connection topologies, and with linear or nonlinear couplings.

We experimentally examine the equivalence between the entropy production evaluated from irreversibility of trajectories and the physical dissipation in dissipative processes via electric resistor-capacitor (RC) circuits. The examinations are performed for two nonequilibrium steady states that are driven by an injected current and temperature difference, respectively. Such an equivalence demonstrates a parameter-free method to evaluate the entropy production of a system. The effects of configurational and temporal resolutions are also studied.

We study experimentally and theoretically the steady-state dynamics of a simple stochastic electronic system featuring two resistor-capacitor circuits coupled by a third capacitor. The resistors are subject to thermal noises at real temperatures. The voltage fluctuation across each resistor can be compared to a one-dimensional Brownian motion. However, the collective dynamical behavior, when the resistors are subject to distinct thermal baths, is identical to that of a Brownian gyrator, as first proposed by R. Filliger and P. Reimann in Physical Review Letters 99, 230602 (2007). The average gyrating dynamics is originated from the absence of detailed balance due to unequal thermal baths. We look into the details of this stochastic gyrating dynamics, its dependences on the temperature difference and coupling strength, and the mechanism of heat transfer through this simple electronic circuit. Our work affirms the general principle and the possibility of a Brownian ratchet working near room temperature scale., Comment: 8 pages, 4 figures

Complex networks have attracted studies from various fields of science due to their relevance in many real systems. As not all nodes are measured in real-systems, this paper explores the effect of the missing nodes on the observed nodes of a bidirectional network with Gaussian noises. Here, it is shown that the collective effect of the missing nodes on the observed nodes may be viewed as a colored noise with exponentially decaying time correlations.

Synchronized bursts (SBs) with complex structures are common in neuronal cultures. Although the origin of SBs is still unclear, they have been studied for their information processing capabilities. Here, we investigate the properties of these SBs in a culture on multi-electrode array system. We find that structures of these SBs are related to the different developmental stages of the cultures. A model based on short term synaptic plasticity, recurrent connections and astrocytic recycling of neurotransmitters has been developed successfully to understand these structures. A phase diagram obtained from this model shows that networks exhibiting SBs are in an oscillatory state due to large enough positive feedback provided by synaptic facilitation and recurrent connections. In this model, the structures of the SBs are the results of intrinsic synaptic interactions; not information stored in the network., 12 pages, 8 figures

Prolonged untreated cardiac alternans may lead to ventricular tachycardia, ventricular fibrillation or sudden cardiac death. Thus, it is important to develop an effective method for controlling alternans. In this paper, the suppression of cardiac alternans is studied using the recently proposed alternating-period feedback control scheme. Numerical simulations are performed on the Luo-Rudy dynamic (LRd) model for single cell. We showed that the action potential duration alternans and intracellular calcium alternans are significantly suppressed after the control is applied. In particular, our result suggests that the contractile force is more balanced from beat to beat after the alternans is reduced.

The optically induced oscillatory response of a spherical two-component, shell-core structured, nanoparticle by nodeless elastic vibrations of soft peripheral shell against hard and dynamically immobile inner core is considered. The eigenfrequencies of the even-parity, spheroidal and odd-parity torsional vibrational modes trapped in the finite-depth shell are obtained which are of practical interest for modal specification of individual resonances in spectra of resonant scattering of long wavelength electromagnetic waves by ultrafine particles., Comment: Surface Review and Letters (World Scientific) Year: 2009 Vol: 16 Issue: 1 (February 2009) Page: 5 - 10

Many sensors (such as low-cost sensors), in essence, display strongly nonlinear dynamic behavior that cannot be calibrated by well-developed linear dynamic compensation methods. So far, no general nonlinear dynamic compensation (NLDC) method exists, although there are some approaches based on nonlinear models (including Volterra series expansion, Wiener kernels, the Hammerstein model, and finite impulse response) that were developed to compensate some special kinds of nonlinear sensors. In this paper, we suggest a general framework for NLDC, in which removal of the influence of disturbance by using an auxiliary sensor is significantly studied and presented. The inverse model and differential-estimation-filter arrays are embedded in this general framework, where a neural network is applied to approximate the inverse mapping, and differential-filter arrays are used to estimate signal differentials up to a certain order. We also discuss the existence conditions of the general framework. The detailed design procedure of this general method is given as well. Simulation and experiments are presented to illustrate the proposed general NLDC method.