Nonperiodic Oscillations Research Articles

Transition from periodic to non-periodic oscillation observed in a mathematical model of bioconvection by motile micro-organisms

Bioconvection observed in a culture of motile micro-organisms was analyzed numerically. The governing equations are the Navier-Stokes equations with the Boussinesq approximation and a diffusion equation for the motile micro-organism. A transition from a static condition to periodic oscillation was observed according to the increase of the Rayleigh number. It was found that the system of bioconvection could be led into chaotic conditions via a single-frequency oscillatory behavior to a sequence of period-doubling bifurcations by increasing the Rayleigh number, which is analogous to Bénard convection.

Inhibitory features of the thermal oxidation of carbon monoxide. A kinetic foundation to dynamic instabilities in closed vessels

Unusual experimental features of the oxidation of carbon monoxide in closed vessels, in which successive ‘ignitions’(non-periodic oscillations) result from a continuous increase of the vessel temperature, are revisited. An isothermal kinetic basis for the interpretation of these events, deduced by numerical methods, is presented. It provides a foundation from which (i) the incomplete spontaneous combustion of CO, discovered more than fifty years ago but not explained hitherto, and (ii) the isothermal oscillatory glows that accompany CO oxidation, may also be interpreted.

Homoclinic phenomena in the gravitational collapse

A class of Bianchi IX cosmological models is shown to have chaotic gravitational collapse, due to Poincaré's homoclinic phenomena. We can program such models so that for any given positive integer N ( N=∞ included) the universe undergoes N non-periodic oscillations (each oscillation requiring a long time) before collapsing. For N=∞ the universe undergoes periodic oscillations.

Nonperiodic forced overflow oscillations in digital filters

Forced overflow oscillations are investigated in a secondorder digital filter whose input sequence is nonperiodic, having been obtained by incommensurably sampling some periodic waveform. Necessary and sufficient conditions are given for the existence of nonperiodic forced overflow oscillations in the digital filter. These conditions are shown to coincide exactly with the corresponding necessary and sufficient conditions for the existence of periodic forced overflow oscillations.

Nonperiodic oscillations having difficulty in synchronizing with an external force in a series‐resonance circuit

Nonperiodic oscillations having difficulty in synchronizing with an external force in a series‐resonance circuit

Chaotic behavior in the Onchidium giant neuron under sinusoidal stimulation

The nonperiodic firing of the Onchidium giant neuron under sinusoidal stimulation is investigated. Attractors obtained stroboscopically show that state points on the attractor are mixed by the baker's transformation. The transition function with period three suggests that the nonperiodic oscillation is chaotic.

Chaos in the self-sustained oscillation of an excitable biological membrane under sinusoidal stimulation

Nonperiodic behavior in self-sustained oscillation of the internodal cell of Nitella was investigated under sinusoidal stimulation. The stroboscopic transformation reveals a single-valued transition function with period three. This suggests that the nonperiodic oscillation is chaotic in the sense of Li and Yorke.

Experiment on Chaotic Responses of a Forced Belousov-Zhabotinsky Reaction

The periodic perturbation is imposed on the Belousov-Zhabotinsky reaction by means of periodically repeated stirring of the reacting mixture. Since the flow of the mixture caused by the stirring includes oxygen gas from the surface, the reaction is modulated by a periodic stirring and an entrained or a nonperiodic oscillation is observed depending on the repetition rate of the stirring. The sample data amplitudes of nonperiodic oscillations are analysed by using the Lorenz plot, and well-defined single-valued transfer functions are obtained which give positive Liapounov numbers and have period three points. We conclude thus that the system exhibits chaotic behavior.

Chaotic States in the Belousov-Zhabotinsky Reaction

Nonperiodic oscillations have been observed in the Belousov-Zhabotinsky reaction in a closed and well-stirred system. By plotting each amplitude (or peak-to-peak value) against the preceding one (Lorenz plot), we obtained well defined single-valued transition functions which allow for a period three. Thus, in the sense of Li and York, we conclude that the system exhibits chaotic behavior.

Periodicity and chaos in great earthquake occurrrence

This paper is an application of the theory of ‘chaos’ to geophysics. It is pointed out that interactions between seismic events may play an important role in causing the apparently random behavior of earthquake occurrence. The great earthquake belt is modeled by a number of large‐scale fault blocks having the same strength and the same interaction parameters. Simulated seismic events show spatiotemporal random behavior if the blocks interact with each other in such a way that when an earthquake occurs in one block, the energy of blocks in the nearest region increases while the energy in the distant blocks decreases. A simple model composed of only two blocks also can exhibit nonperiodic behavior, if the blocks mutually interact in such a way that when an earthquake occurs in one block, the rate of energy increase decreases in the other block. An electrical analog model of the coupled fault blocks showing nonperiodic oscillation is presented.

A microscopic model for catalytic surfaces—I. Catalytic wires and gauzes

A new “fuzzy wire” model of catalytic wires and gauzes is presented which is in good agreement with observed ignition, extinction, and flickering phenomena. The model predicts both simple harmonic oscillations as well as a wide variety of nonperiodic chaotic oscillations. Quantitative comparisons with data for butane oxidation and cyclohexene oxidation are quite good; however, the very long period oscillations observed for H 2 and CO oxidation are not predicted by the simplest forms of the model.

An experimental study of multiple peak periodic and nonperiodic oscillations in the Belousov–Zhabotinskii reaction

Experiments have been carried out on the Belousov–Zhabotinskii reaction in an isothermal continuous stirred tank reactor. The flow rate was varied from low values where simple single peak oscillations occur to large values where the reactor is in steady state. Several types of periodic multipeak oscillations were observed. Three regions of nonperiodic behavior were found, each of which occurred in a well defined range of flow rates bracketed by periodic oscillations.

Influence of a One-Dimensional Superlattice on a Two-Dimensional Electron Gas

We report unusual structure in the dc conductivity below 4.2 K as well as nonperiodic oscillations in the magnetoconductance of a two-dimensional electron gas in Si at low magnetic fields. A model of a superlattice with a gap which varies with carrier density is proposed to interpret the results. The superlattice appears to be of a somewhat general nature although the cause is not yet known.

Nonlinear Aspects of Competition Between Three Species

It is shown that for three competitors, the classic Gause–Lotka–Volterra equations possess a special class of periodic limit cycle solutions, and a general class of solutions in which the system exhibits nonperiodic population oscillations of bounded amplitude but ever increasing cycle time. Biologically, the result is interesting as a caricature of the complexities that nonlinearities can introduce even into the simplest equations of population biology ; mathematically, the model illustrates some novel tactical tricks and dynamical peculiarities for 3-dimensional nonlinear systems.

Filtres passe-bande chimiques et oscillations non periodiques

In this note some of the basic hypotheses used by N. Rashevsky in his studies of non-periodic oscillations in cerebral wave patterns ( Bull. Math. Biophys., Vol. 33, 1971) are reconsidered. The concept of chemical pass-band filters is suggested to develop models which account for several aspects of the electrical cortex activity rhythms. A very simple system is then used to demonstrate that certain non-linearities might explain the disappearance of the alpha rhythm as well as the appearance of waves at different frequencies.

A note on sporadic nonperiodic oscillations in the activity of the endocrine system and on the endocrine-nervous system feedback.

By generalizing a previous paper on periodicities in the endocrine system (Bull. Math. Biophysics,30, 735–749, 1968), it is shown that nonperiodic, sporadic oscillations in the system are also possible. A procedure of describing the feedback mechanism between the endocrine system and the central nervous system is suggested. It is shown that the combined system: endocrine—CNS, also may show sporadic fluctuations.

Sporadic sustained nonperiodic oscillations in the activities of organismic sets.

In combining the author's theories of organismic sets (Rashevsky,Bull. Math. Biophysics,31, 159–198, 1969a) and Robert Rosen's theory of (M, R)-systems (Bull. Math. Biophysics,20, 245–265, 1958), a conclusion is reached that the number of either normal or pathological phenomena in organismic sets may occur. Those phenomena are characterized by occurring spontaneously once in a while but are not exactly periodic. Some epilepsies are an example of such pathological phenomena in the brain.

Mathematical biophysics of sustained nonperiodic oscillations of excitation and inhibition in the central nervous system.

There are a number of phenomena in the central nervous system which are not periodic in the strict sense of the word. The simplest example is the α-rhythm which represents an oscillation that is not strictly periodic in a mathematical sense. Some diseases like periodic relapsing catatonia or the manic-depressive psychoses are almost strictly periodical but such phenomena as attacks of epilepsy repeat themselves perhaps at average intervals but those intervals are not equal and are not predictable. We consider that even such phenomena like a fit of creative work has the same mechanism. All those phenomena deal with sporadic spontaneous nonperiodic overexcitation of certain parts of the brain. Depending on which part of the brain is overexcited, we might have either a grand or a petit mal epilepsy, or a fit of creativity.

A note on nonperiodic undamped oscillations, with special reference to brain waves.

Nonperiodical sustained fluctuations of electrical potential are characteristic of the rhythms of cortical electric activities. A nonperiodical negatively or positively damped oscillation would be a general solution of any first order linear system of differential equations. Attention is called to a somewhat specialized type of a system of ordinary linear differential equations, which are used by Vito Volterra (Lecons Sur la Theorie Mathematique de la Lutte Pour la Vie, Paris, Gauthier-Villars, 1931) in his theory of interdevouring species. This system of linear equations leads to nonperiodicalundamped oscillations and admits several plausible interpretations in terms of possible biophysical reactions in the brain. A number of new problems is posed and discussed by this study.

On sea level, temperature, and salinity variations in the central tropical Pacific and on Pacific Ocean islands

Spectrums of oceanographic and meteorological variables are investigated for the frequency range between zero and six cycles per year. It is found that the root mean square amplitudes of the annual and nonperiodic oscillations are of the same order of magnitude. Sea level changes at neighboring islands are coherent and in phase. Changes at distant islands are coherent only at low frequencies, and their phase depends upon whether the islands are affected by the same wind regime. There is a strong and direct relation between changes of sea level and of sea temperature at low frequencies, but there is no relation between changes of sea level and of atmospheric pressure. Air temperature and sea temperature oscillations are directly related to each other, except where rainfall affects the former, in which case there is no relation. In the intratropical convergence zone a significant and inverse relation exists between air temperature and rainfall. Salinity and rainfall fluctuations are related inversely to each other, but the coherence varies considerably from island to island. Sea temperature and wind speed oscillations are related inversely to each other in the NE trade wind region. The statistical results from the island station analysis are in fair agreement with those obtained from largescale hydrographic surveys.