Logarithmic gaps have been used in order to find a periodic component of the sequence of prime numbers, hidden by a random noise (stochastic or chaotic). It is shown that multiplicative nature of the noise is the main reason for the successful application of the logarithmic gaps transforming the multiplicative noise into an additive one. A relation of this phenomenon to spontaneous neuron activ...

Logarithmic gaps have been used in order to find a periodic component of the sequence of prime numbers, hidden by a random noise stochastic or chaotic . It is shown that multiplicative nature of the noise is the main reason for the successful application of the logarithmic gaps transforming the multiplicative noise into an additive one. A relation of this phenomenon to spontaneous neuron activi...

Many chaotic oscillators have rather coherent phase dynamics but strong fluctuation in the amplitudes. Conversely, homoclinic chaos is characterized by quite regular spikes but strong fluctuation in their time intervals. We study the effects of noise on the synchronization of homoclinic chaos to a weak periodic signal and demonstrate numerically and experimentally in a CO2 laser system that noi...

Stochastic Resonance in a coupled FitzHugh-Nagumo equation is investigated. The optimal noise intensity and the optimal input frequency, which maximize the signal to noise ratio of the output signal, are studied numerically, and their dependence on system parameters and connection coe cients is examined. It is found that a network composed of six elements can separate a superimposed periodic pu...

The influence of additive noise, multiplicative noise, and higher-order effects on exploding solitons in the framework of the prototype complex cubic-quintic Ginzburg-Landau equation is studied. Transitions from explosions to filling-in to the noisy spatially homogeneous finite amplitude solution, collapse (zero solution), and periodic exploding dissipative solitons are reported.