Irrational phase synchronization

Experimental study of the irrational phase synchronization of coupled nonidentical mechanical metronomes

It has recently been observed in numerical simulations that the phases of two coupled nonlinear oscillators can become locked into an irrational ratio, exhibiting the phenomenon of irrational phase synchronization (IPS) [Phys. Rev. E 69, 056228 (2004)]. Here, using two coupled nonidentical periodic mechanical metronomes, we revisit this interesting phenomenon through experimental studies. It is demonstrated that under suitable couplings, the phases of the metronomes indeed can become locked into irrational ratios. Numerical simulations confirm the experimental observations and also reveal that in the IPS state, the system dynamics are chaotic. Our studies provide a solid step toward further studies of IPS.

Collective almost synchronisation in complex networks

This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it.

Transmission of information in active networks

Shannon's capacity theorem is the main concept behind the theory of communication. It says that if the amount of information contained in a signal is smaller than the channel capacity of a physical media of communication, it can be transmitted with arbitrarily small probability of error. This theorem is usually applicable to ideal channels of communication in which the information to be transmitted does not alter the passive characteristics of the channel that basically tries to reproduce the source of information. For an active channel, a network formed by elements that are dynamical systems (such as neurons, chaotic or periodic oscillators), it is unclear if such theorem is applicable, once an active channel can adapt to the input of a signal, altering its capacity. To shed light into this matter, we show, among other results, how to calculate the information capacity of an active channel of communication. Then, we show that the channel capacity depends on whether the active channel is self-excitable or not and that, contrary to a current belief, desynchronization can provide an environment in which large amounts of information can be transmitted in a channel that is self-excitable. An interesting case of a self-excitable active channel is a network of electrically connected Hindmarsh-Rose chaotic neurons.

Experimental observation of synchronous competition in the Chua system

We present experimental results for two different sinusoidal functions competing to phase synchronize a Chua oscillator. Our approach involves real-time observation of the synchronization process. It shows that depending on the amplitude and frequency values of the two sinusoidal functions, the Chua oscillator can stay phase synchronized to one or the other of the inputs all the time or can alternate synchronous states between them. Numerical simulations show good agreement with the experimental observations.

Randomization of the Fourier transform

We have investigated the multiplicity and complexity in eigenvalues of the fractional Fourier transform and found that the ambiguity of the eigenvalues may indicate randomness. We have therefore proposed a method to randomize the Fourier transform. Such a random Fourier transform can be applied in the field of image encryption and decryption.