The design of analogue electronic experiments to investigate phenomena in nonlinear dynamics, especially stochastic phenomena, is described practical terms. advantages and disadvantages this approach, comparison more conventional digital methods, are discussed. It pointed out that simulation provides a simple, inexpensive, technique easily applied any laboratory facilitate the implementation complicated expensive experimental projects; there some important problems for which methods have so...

We consider the stochastic dynamics of escape in an excitable system, FitzHugh-Nagumo (FHN) neuronal model, for different classes excitability. discuss, first, threshold structure FHN model as example a system without saddle state. then develop nonlinear (nonlocal) stability approach based on theory large fluctuations, including finite-noise correction, to describe noise-induced regime. show that is revealed via patterns most probable (optimal) fluctuational paths. The allows us estimate...

Stochastic resonance (SR), a phenomenon in which periodic signal nonlinear system can be amplified by added noise, is introduced and discussed. Techniques for investigating SR using electronic circuits are described practical terms. The physical nature of SR, the explanation weak-noise as linear response phenomenon, considered. Conventional systems characterized static bistable potentials, together with examples data obtainable from circuit models used to test theory.

We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms set polynomial basis functions representing force governing system oscillations. The strength and direction coupling noise intensity are simultaneously inferred from univariate blood pressure signal. Our new inference technique does not require extensive global optimization, it is applicable to wide range complex dynamical systems subject noise.

A different form of stochastic resonance, in which the weak periodic force is applied multiplicatively (rather than additively) noise, has been investigated for a Brownian particle moving double-well potential. regular signal whose amplitude increases sharply with increasing noise intensity shown to arise when potential asymmetric.$---- The experimental measurements are good agreement theoretical analysis.

We investigate, theoretically and by analog experiment, the distribution of paths for large fluctuations away from a stable state. have found critical broadening coming to cusp point that represents simplest generic singularity in pattern most probable (optimal) fluctuational nonequilibrium systems. The behavior can be described Landau-type theory. predict observe two-ridged distributions arrivals on switching line separates areas reached along optimal different types.

The kinetics of a periodically driven nonlinear oscillator, bistable in nearly resonant field, has been investigated theoretically and through analog experiments. An activation dependence the probabilities fluctuational transitions between coexisting attractors observed, energies have calculated measured for wide range parameters. position kinetic phase transition (KPT), at which populations are equal, established. A critical phenomena is shown to arise vicinity KPT including, particular,...

Topologies of invariant manifolds and optimal trajectories are investigated in stochastic continuous systems maps. A topological method is introduced that simplifies the solution boundary value problems: The activation energy calculated as a function set parameters characterizing initial conditions escape path. applied explicitly to compute path for variety dynamical

We discuss activated escape from a metastable state of system driven by time-periodic force. show that the probabilities can be changed very strongly even comparatively weak In broad parameter range, activation energy depends linearly on force amplitude. This dependence is described logarithmic susceptibility, which analyzed theoretically and through analog digital simulations. A closed-form explicit expression for rate an overdamped Brownian particle presented shown to in quantitative...

A mathematical model of the cardiovascular system is simulated numerically. The basic unit in an oscillator that possesses a structural stability and robustness motivated by physiological understanding analysis measured time series. Oscillators with linear couplings are found to reproduce main characteristic features experimentally obtained spectra. To explain variability cardiac respiratory frequencies, however, it essential take into account rest system, i.e. consider effect noise. It...

A self-consistent analytic approach is introduced for the estimation of access resistance and current through an open ion channel arbitrary number species. For flowing radially inward from infinity to mouth, Poisson-Boltzmann-Nernst-Planck equations are solved analytically in bulk with spherical symmetry three dimensions, by linearization. Within channel, Poisson-Nernst-Planck equation a one-dimensional approximation. An iterative procedure used match two solutions together at mouth way. It...

The rising number of small unmanned aerial vehicles (UAVs) expected in the next decade will enable a new series commercial, service, and military operations low altitude airspace as well above densely populated areas. These may include on-demand delivery, medical transportation services, law enforcement operations, traffic surveillance many more. Such unprecedented scenarios create need for robust, efficient ways to monitor UAV state time guarantee safety mitigate contingencies throughout...

An algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach analytical; consequently, the resulting does not require an extensive global search model parameters, provides optimal compensation effects of noise, and robust a broad range models. strengths are illustrated by inferring parameters Lorenz system comparing results with those earlier research. efficiency accuracy further demonstrated five globally locally coupled oscillators.

We report self-consistent Brownian dynamics simulations of a simple electrostatic model the selectivity filters (SF) calcium ion channels. They reveal regular structure in conductance and as functions fixed negative charge Qf at SF. This consists distinct regions high (conduction bands) M0, M1, M2 separated by zero-conductance (stop-bands). Two these conduction bands, M1 M2, demonstrate prominent anomalous mole fraction effects can be identified with L-type RyR

We use Brownian dynamics (BD) simulations to study the ionic conduction and valence selectivity of a generic electrostatic model biological ion channel as functions fixed charge ${Q}_{f}$ at its filter. are thus able reconcile discrete calcium bands recently revealed in our BD simulations, M0 (${Q}_{f}=1e$), M1 (3$e$), M2 (5$e$), with set sodium L0 (0.5$e$), L1 (1.5$e$), thereby obtaining completed pattern vs for sodium-calcium channels family. An increase leads an selectivity:...


 Safety of the next-generation space flight vehicles requires development an in-flight Failure Detection and Prognostic (FD&P) system. Development such system is challenging task that involves analysis many hard hitting engineering problems across board. In this paper we report progress in FD&P for re-contact fault between upper stage nozzle inter-stage caused by first separation failure. A high-fidelity models analytical estimations are applied to analyze following sequence...

The first measurements of an exit location distribution are reported for overdamped nonconservative system perturbed by weak white noise, modeled both numerically and analog electronic circuit. In the weak-noise limit is increasingly concentrated near a saddle point dynamics well approximated Weibull distribution, in agreement with theoretical predictions. A physical explanation this behavior given, which should facilitate computation corrections to limiting form.

We consider a noise-driven exit from domain of attraction in two-dimensional bistable system lacking detailed balance. Through analog and digital stochastic simulations, we find theoretically predicted bifurcation the most probable path as parameters are changed, corresponding nonanalyticity generalized activation energy. also investigate extent to which is related local breaking time-reversal invariance.

The energy-optimal entraining of the dynamics a periodically driven oscillator, moving it from chaotic attractor to coexisting stable limit cycle, is investigated via analysis fluctuational transitions between two states. deterministic optimal control function identified with corresponding force, which found by numerical and analog simulations.

Fluctuational escape from a multiwell potential is shown to display new features, as compared the conventional single-well case. The flux J may depend on friction gamma exponentially strongly, over an long period; for small enough temperatures, J(gamma) undergoes marked oscillations in range of gamma, and time evolution changes drastically exceeds critical value.