The verification of the digital models of chaotic systems and processes is a valuable problem in many practical applications, such as nonlinear control and communications. In our study, we propose a hybrid technique for chaotic systems’ identification, based on the chaotic synchronization of digital and analog counterparts and a numerical optimization method used for the fine tuning of parameters. An analog circuit implementing the Rössler oscillator with digitally controlled parameters was chosen as an identification object, and the FPGA model was used as a digital counterpart for coupling and parameter retrieval. The synchronization between analog and digital chaotic models can be used to estimate the quality of an identification procedure. The results of this study clarify the practical bounds of digital and analog systems’ equivalence. They also contribute to the problem of designing technical systems possessing advantages of both analog and digital chaotic generators (e.g., a high accuracy and protection from quasi-chaotic oscillation modes).

The vulnerability of chaotic communication systems to noise in transmission channel is a serious obstacle for practical applications. Traditional signal processing techniques provide only limited possibilities for efficient filtering broadband chaotic signals. In this paper, we provide a comparative study of several denoising and filtering approaches: a recursive IIR filter, a median filter, a wavelet-based denoising method, a method based on empirical modes decomposition, and, finally, propose the new filtering algorithm based on the cascade of driven chaotic oscillators. Experimental results show that all the considered methods make it possible to increase the permissible signal-to-noise ratio to provide the possibility of message recognition, while the new proposed method showed the best performance and reliability.

In many tasks related to realistic neurons and neural network simulation, the performance of desktop computers is nowhere near enough. To overcome this obstacle, researchers are developing FPGA-based simulators that naturally use fixed-point arithmetic. In these implementations, little attention is usually paid to the choice of numerical method for the discretization of the continuous neuron model. In our study, the implementation accuracy of a neuron described by simplified Hodgkin–Huxley equations in fixed-point arithmetic is under investigation. The principle of constructing a fixed-point neuron model with various numerical methods is described. Interspike diagrams and refractory period analysis are used for the experimental study of the synthesized discrete maps of the simplified Hodgkin–Huxley neuron model. We show that the explicit midpoint method is much better suited to simulate the neuron dynamics on an FPGA than the explicit Euler method which is in common use.

Composition methods are an effective way to obtain ODE solvers of high accuracy order along with extrapolation and Runge-Kutta formulas. This paper considers theoretical layouts and experimental research of semi-implicit composition methods of different order applied to the simulation of chaotic dynamical systems. The comparison of stability regions is given for semi-implicit and implicit midpoint composition methods with different order of accuracy. Two chaotic test problems are considered: Lorenz attractor system and Sprott Case G system. An alternative way to estimate local truncation error for semi-implicit adaptive solvers is described. A performance of various numerical integration methods was compared by plotting computational costs via truncation error. This comparison shows that semi-implicit composition methods can be more computationally effective for chaotic problems solution than traditional solvers.

This paper considers two approaches to hydroacoustic signal classification, taking the sounds made by whales as an example: a method based on harmonic wavelets and a technique involving deep learning neural networks. The study deals with the classification of hydroacoustic signals using coefficients of the harmonic wavelet transform (fast computation), short-time Fourier transform (spectrogram) and Fourier transform using a kNN-algorithm. Classification quality metrics (precision, recall and accuracy) are given for different signal-to-noise ratios. ROC curves were also obtained. The use of the deep neural network for classification of whales’ sounds is considered. The effectiveness of using harmonic wavelets for the classification of complex non-stationary signals is proved. A technique to reduce the feature space dimension using a ‘modulo N reduction’ method is proposed. A classification of 26 individual whales from the Whale FM Project dataset is presented. It is shown that the deep-learning-based approach provides the best result for the Whale FM Project dataset both for whale types and individuals.

Numerical simulation of nonlinear dynamical systems with the chaotic behavior is the major research field in a modern computer science. The aim of this research was the experimental study of new symmetric numerical integration method as a basic method for the Aitken-Neville extrapolation scheme. The properties of the Sprott (B) chaotic nonlinear system was studied via computer simulation, and the global truncation error was analyzed for the extrapolation methods of accuracy order 4 and 6. Some conclusions about the advantages of proposed symmetric ODE solver compared to the classical Runge-Kutta and Gregg-Bulirsch-Stoer methods are given. The considered extrapolation scheme has a single-step semi-implicit method as a basic solver, and is more numerically effective while being implemented on parallel computers.