Xing Pei

Homoclinic bifurcation in a Hodgkin-Huxley model of thermally sensitive neurons.

We study global bifurcations of the chaotic attractor in a modified Hodgkin-Huxley model of thermally sensitive neurons. The control parameter for this model is the temperature. The chaotic behavior is realized over a wide range of temperatures and is visualized using interspike intervals. We observe an abrupt increase of the interspike intervals in a certain temperature region. We identify this as a homoclinic bifurcation of a saddle-focus fixed point which is embedded in the chaotic attractors. The transition is accompanied by intermittency, which obeys a universal scaling law for the average length of trajectory segments exhibiting only short interspike intervals with the distance from the onset of intermittency. We also present experimental results of interspike interval measurements taken from the crayfish caudal photoreceptor, which qualitatively demonstrate the same bifurcation structure. (c) 2000 American Institute of Physics.

Low-Dimensional Dynamics in Sensory Biology 1: Thermally Sensitive Electroreceptors of the Catfish

We report the results of a search for evidence of periodic unstableorbits in the electroreceptors of the catfish. The function of thesereceptor organs is to sense weak external electric fields. Inaddition, they respond to the ambient temperature and to the ioniccomposition of the water. These quantities are encoded by receptorsthat make use of an internal oscillator operating at the level of themembrane potential. If such oscillators have three or more degreesof freedom, and at least one of which also exhibits a nonlinearity,they are potentially capable of chaotic dynamics. By detecting theexistence of stable and unstable periodic orbits, we demonstratebifurcations between noisy stable and chaotic behavior using theambient temperature as a parameter. We suggest that the techniquedeveloped herein be regarded as an additional tool for the analysisof data in sensory biology and thus can be potentially useful instudies of functional responses to external stimuli. We speculatethat the appearance of unstable orbits may be indicative of a stateof heightened sensory awareness by the animal.

THE PADDLEFISH ROSTRUM FUNCTIONS AS AN ELECTROSENSORY ANTENNA IN PLANKTON FEEDING

A novel electrosensory function is presented for the large, plankton–feeding, freshwater paddlefish, Polyodon spathula, along with a hypothesis which accounts for the distinctive, elongated rostrum of this unusual fish. Behavioural experiments conducted in the ‘dark’ (under infrared illumination), to eliminate vision, show that paddlefish efficiently capture planktonic prey to distances up to 80–90 mm. They make feeding strikes at dipole electrodes in response to weak low–frequency electrical currents. Fish also avoid metal obstacles placed in the water, again in the dark. Electrophysiological experiments confirm that the Lorenzinian ampullae of paddlefish are sensitive to weak, low–frequency electrical signals, and demonstrate unequivocally that they respond to the very small electrical signals generated by their natural zooplankton prey (Daphnia sp.). We propose that the rostrum constitutes the biological equivalent of an electrical antenna, enabling the fish to accurately detect and capture its planktonic food in turbid river environments where vision is severely limited. The electrical sensitivity of paddlefish to metallic substrates may interfere with their migrations through locks and dams.

Low-Dimensional Dynamics in Sensory Biology 2: Facial Cold Receptors of the Rat

We report the results of a search for evidence of unstable periodic orbits in the sensory afferents of the facial cold receptors of the rat. Cold receptors are unique in that they exhibit a diversity of action potential firing patterns as well as pronounced transients in firing rate following rapid temperature changes. These characteristics are the result of an internal oscillator operating at the level of the membrane potential. If such oscillators have three or more degree of freedom, and at least one of which also exhibits a nonlinearity, they are potentially capable of complex activity. By detecting the existence of unstable periodic orbits, we demonstrate low-dimensional dynamical behavior whose characteristics depend on the temperature range, impulse pattern, and temperature transients.

The detection threshold, noise and stochastic resonance in the Fitzhugh-Nagumo neuron model☆

Abstract In a class of experiments in sensory biology sub- or slightly supra-threshold stimuli are applied at the periphery while making action potential recordings at a higher level in the nervous system. In many cases the records are largely noise but with a small coherence with the stimulus. The detection threshold for increasing stimulus intensity is frequently measured, and this threshold can often be controlled by manipulating some additional biological parameter, for example, the temperature or inherent noise intensity. How does this parameter change the detection threshold? In this note, we test three popular paradigms on an electronic Fitzhugh-Nagumo neuron model and compare the results with a simple threshold theory.

Noise-induced impulse pattern modifications at different dynamical period-one situations in a computer model of temperature encoding.

We used a minimal Hodgkin-Huxley type model of cold receptor discharges to examine how noise interferes with the non-linear dynamics of the ionic mechanisms of neuronal stimulus encoding. The model is based on the assumption that spike-generation depends on subthreshold oscillations. With physiologically plausible temperature scaling, it passes through different impulse patterns which, with addition of noise, are in excellent agreement with real experimental data. The interval distributions of purely deterministic simulations, however, exhibit considerable differences compared to the noisy simulations especially at the bifurcations of deterministically period-one discharges. We, therefore, analyzed the effects of noise in different situations of deterministically regular period-one discharges: (1) at high-temperatures near the transition to subthreshold oscillations and to burst discharges, and (2) at low-temperatures close to and more far away from the bifurcations to chaotic dynamics. The data suggest that addition of noise can considerably extend the dynamical behavior of the system with coexistence of different dynamical situations at deterministically fixed parameter constellations. Apart from well-described coexistence of spike-generating and subthreshold oscillations also mixtures of tonic and bursting patterns can be seen and even transitions to unstable period-one orbits seem to appear. The data indicate that cooperative effects between low- and high-dimensional dynamics have to be considered as qualitatively important factors in neuronal encoding.

Interactions between slow and fast conductances in the Huber/Braun model of cold-receptor discharges

Abstract Transitions between different types of impulse patterns, according to experimentally recorded cold-receptor discharges, can successfully be mimicked with a minimal Hodgkin–Huxley-type simulation, here referred to as the Huber/Braun cold-receptor model. The model consists of two sets of simplified de- and repolarizing ionic conductances responsible for spike generation and slow-wave potentials, respectively. Over a broad temperature range, spike patterns are determined by the periodicity of subthreshold oscillations. At low temperatures, however, the periodicity of the pattern is destroyed and then appears again but with different patterns of different rhythmicity. We demonstrate that these complex transitions originate from the interactions between slow-wave and spike-generating currents.

Finding unstable periodic orbits in electroreceptors, cold receptors and hypothalamic neurons☆

Abstract Recently, searches for low-dimensional dynamical activity in various biological preparations have become fashionable. In particular, demonstrations of the existence of unstable periodic orbits (UPOs) and bifurcations between unstable and stable states are of interest. Here, we report the detection of UPOs in three diverse preparations: electroreceptor, cold receptor and hypothalamic neurons. Inherent, noise mediated oscillators are common to these temperature sensitive neurons, and the UPOs arise in them in the absence of external periodic stimulation. The external temperature is the bifurcation parameter. Behaviors in response to temperature transients are also shown.

Stochastic synchronization of electroreceptors in paddlefish

We studied synchronization of electrosensitive cells of the paddlefish by means of electrophysiological experiments. We found that primary afferents of the paddlefish are represented by noisy nonlinear oscillators. Different types of phase locked regimes are observed. The influence of internal noise is discussed.

Counting unstable periodic orbits in noisy chaotic systems: A scaling relation connecting experiment with theory.

The experimental detection of unstable periodic orbits in dynamical systems, especially those which yield short, noisy or nonstationary data sets, is a current topic of interest in many research areas. Unfortunately, for such data sets, only a few of the lowest order periods can be detected with quantifiable statistical accuracy. The primary observable is the number of encounters the general trajectory has with a particular orbit. Here we show that, in the limit of large period, this quantity scales exponentially with the period, and that this scaling is robust to dynamical noise. (c) 1998 American Institute of Physics.