We investigate how stochastic Poisson impulsive forcing influences the spatiotemporal dynamics of a two-dimensional network of Hindmarsh-Rose neurons. Unlike continuous noise, impulsive forcing introduces discrete, state-dependent perturbations, making the system response highly sensitive to both the statistics and the spatial structure of the input. In most of the parameter space, stochastic impulses destabilize the initial coherent spiral-wave regime and lead to unstable spiral-wave activity. At the same time, they can also produce constructive effects. Both spatially uniform and spatially non-uniform forcing induce stable target waves that are absent in the autonomous system, suggesting a common mechanism of structure formation driven by discrete excitation events. In addition, spatially uniform forcing suppresses spatial heterogeneity and leads to coherent, nearly synchronous oscillations, demonstrating that even random impulses can promote global synchronization. By contrast, spatially uncorrelated forcing enhances front fragmentation and incoherence, especially at higher amplitudes. To identify and compare the resulting regimes in a highly multistable parameter space, we use a feature-based clustering approach based on statistical descriptors of wave morphology and evolution across multiple time scales. This results in a clear separation of physically distinct regimes. Overall, stochastic Poisson impulses serve not only as a source of disorder but also as an effective control mechanism for destabilizing, reorganizing, and synchronizing collective wave dynamics in networks of coupled neuronal oscillators.

The phenomenon of energy localization in nonlinear lattices is of interest to both fundamental science and crystal physics. Localized energy can help overcome potential barriers to defect migration or initiation, which is a topic of significant scientific and practical importance. In real lattices, such as crystal lattices, the presence of inevitable perturbations necessitates a shift in research focus from finding exact discrete breather solutions towards the long-lived quasi-breather (qB) solutions. Higher-dimensional lattices support different qBs with different symmetries, and it is important to know the conditions for their existence. In crystals, long-range interactions, such as metallic or Coulomb interactions, can play an important role. In the present work, the search for qBs in the square beta-FPUT lattice is continued, taking into account interactions up to the fourth neighbor. The search for qBs is carried out under the assumption that the stiffness of the bonds decreases with their length, as is expected for chemical bonds in crystals. New qBs are identified in comparison to the lattice with short interactions, and it is demonstrated that some of them can move along the lattice, transporting energy.

We study the effect of Levy noise on phase synchronization in adaptive ensembles of excitable elements. We consider an ensemble of FitzHugh-Nagumo neurons with nonlocal coupling and a ring topology, under the external additive alpha-stable Levy noise. A key feature of the model is the adaptive coupling tuning mechanism, which adjusts the strength of interactions between neurons based on a moving average of the interspike interval. The coupling strength increases during spikes with a large interspike interval and decreases during synchronous spikes, which allows the network to automatically adjust the minimum necessary total coupling strength to maintain a coherent regime even under strong noise with heavy distribution tails. We found that the coherent resonance characteristic of a single neuron is also observed in a coupled system. However, the optimal noise intensity shifts to lower values as the coupling range increases. Synchronization is achieved only at a certain coupling range, while at a lower coupling range only cluster synchronization is possible even with strong coupling of neurons. Levy noise requires a stronger global interaction between neurons to achieve synchronization compared to Gaussian noise. However, the positive asymmetry of the noise distribution significantly reduces this threshold due to the increased sensitivity of neurons to positive fluctuations. The proposed adaptive mechanism successfully ensures synchronization of the system in the entire studied range of Levy noise parameters and connection topology, demonstrating the versatility, high adaptation speed and energy efficiency of the approach. The obtained results open up new possibilities for controlled coordination of spatiotemporal dynamics in neural and other nonlinear excitable systems under extreme stochastic influences.

It is well known that a modulationally unstable short-wavelength delocalized nonlinear vibrational mode (DNVM) can create chaotic discrete breathers (DBs) in a nonlinear lattice. A necessary condition for this is that the DNVM must have a frequency outside the phonon spectrum of the lattice. This phenomenon has been repeatedly analyzed for one- and two-dimensional lattices, and here it is studied for a bcc lattice with β-Fermi–Pasta–Ulam–Tsingou potential. Using the group-theoretical approach developed by Chechin and Sakhnenko, four DNVMs are found with a wave vector at the boundary of the first Brillouin zone and frequencies above the phonon spectrum. It is shown that the development of the modulational instability of all four DNVMs with amplitudes above a certain value leads to the formation of chaotic DBs, which is justified by calculating the energy localization parameter and the maximum particle energy. Chaotic DBs in the three-dimensional bcc lattice radiate their energy faster than in previously studied two-dimensional lattices. The results obtained describe one of the possible mechanisms of energy dissipation by a crystal lattice in a far-from-equilibrium system.

We investigate a spike activity of a network of excitable FitzHugh-Nagumo neurons, which is under constant two-frequency auditory signals. The neurons are supplemented with linear frequency filters and nonlinear input signal converters. We show that it is possible to configure the network to recognize a specific frequency ratio (musical interval) by selecting the parameters of the neurons, input filters, and coupling between neurons. A set of appropriately configured subnetworks with different topologies and coupling strengths can serve as a classifier for musical intervals. We have found that the selective properties of the classifier are due to the presence of a specific topology of coupling between the neurons of the network.

It is known that the modulational instability of a delocalized nonlinear vibrational mode (DNVM) with frequency outside the phonon band can lead to spontaneous energy localization in a nonlinear lattice on chaotic discrete breathers (CDBs). Considering a β-FPUT square lattice with nearest and next-nearest interactions, the appearance of CDBs is analyzed for different stiffnesses of the first- and second-nearest interactions, k1 and k2, keeping the density of the lattice unchanged. There are two DNVMs in the square lattice with frequencies above the phonon spectrum and both are studied. The appearance of CDBs in the lattice is monitored by calculating the time evolution of the energy localization parameter L and the maximum energy of the particles emax. For solid state physics and materials science, the important range of stiffness parameters is k2k1/4. This means that they can form in crystals if the stiffness of the second-neighbor bonds is smaller than that of the first-neighbor bonds, but not too small. Depending on the relation between the anharmonicity parameters of the first- and second-neighbor bonds CDBs can have different polarization.

В рамках данного исследования проведен детальный анализ волновых процессов в двумерной структуре черного фосфорена под воздействием непрерывного продольного сжатия. Это сжатие осуществлялось строго в двух кристаллографических ориентациях фосфорена – либо в направлении "зигзаг", либо в направлении "кресла". Сложная атомная геометрия фосфорена, значительно отличающаяся от структуры графена, вносит дополнительные особенности в динамику распространения волн, возникающих в материале в результате сжатия. Для моделирования динамических явлений были применены методы молекулярной динамики. Процесс возбуждения акустических и ударных волн был инициирован с помощью сжимающего поршня, движущегося с постоянной заданной скоростью. В ходе исследования был проведен детальный анализ распространения волнового фронта на атомном уровне. В рамках этого анализа были изучены колебания атомов, проходящих через волны, и изменения энергетических параметров атомов и волны в зависимости от скорости движения поршня. Полученные результаты вносят вклад в понимание нелинейных волновых процессов в двумерных материалах и расширяют представления о поведении волн в сложных геометрических кристаллических структурах. Это исследование помогает получить более глубокое понимание механизмов распространения и эволюции ударных и акустических волн в таких материалах, как фосфорен, и имеет важное значение для разработки новых наноматериалов и технологий. Полученные результаты расширяют наше понимание динамики материалов на атомном уровне и могут найти практическое применение в области нанотехнологий и разработке новых материалов с улучшенными свойствами.

We present numerical results on the effects of two presynaptic FitzHugh-Nagumo neurons on a postsynaptic neuron under unidirectional electrical coupling. The presynaptic neurons affect the postsynaptic neuron not simultaneously but with a certain time shift. We consider cases where the amplitudes of the presynaptic spikes can be both higher and lower than the excitation threshold level. The latter case receives the main attention in our work. We carefully examine the conditions under which the postsynaptic neuron is excited by the two asynchronous external spikes. With arbitrarily chosen parameters, the FitzHugh-Nagumo neuron is almost incapable of accumulating the energy of external signals, unlike, for example, the leaky integrate-and-fire neuron. In this case, the postsynaptic neuron only excites with a very short time delay between external impulses. However, we have discovered, for the first time, a parameter region where neuron excitation is possible even with significant time delays between presynaptic impulses with subthreshold amplitudes. We explain this effect in detail and describe the mechanism behind its occurrence. We identify the boundaries of this region in the parameter plane of time delay and coupling coefficient by varying the control parameter values of the neurons. The FitzHugh-Nagumo neuron has not previously been used as a node in spiking neural networks for training via spike-timing-dependent plasticity due to the lack of an integrate-and-fire effect. However, the detection of a certain range of parameters makes the potential application of this neuron for STDP training possible.

We present numerical results for the effects of influence by high-amplitude periodic pulse series on a network of nonlocally coupled Hindmarsh-Rose neurons with 2D geometry of the topology. We consider the case when the pulse amplitude is larger than the amplitude of oscillations in the autonomous network fora wide range of pulse frequencies. An initial regime in the network is a spiral wave chimera. We show that the effects of external influence strongly depend on a balance between the pulse frequency and frequencies of the spectral peaks of the autonomous network. Except for the destructive role of the pulses, when they lead to loss of stability of the initial regime, we have also revealed a constructive role. We have found for the first time the emergence of anew type of multi-front spiral waves, when the wavefront represents a set of several close fronts, and the wave dynamics are significantly different from common spiral waves: neurons oscillate independently to the wave rotation, the rotation velocity is in many times less than for the common spiral wave, etc. We have also discovered several types of cluster spatiotemporal structures induced by the pulses.

We study the spike activity of two mutually coupled FitzHugh – Nagumo neurons, which is influenced by two-frequency signals. The ratio of frequencies in the external signal corresponds to musical intervals (consonances). It has been discovered that this system can exhibit selective properties for identifying musical intervals. The mechanism of selectivity is shown, which is associated with the influence on the spiking frequency of neurons by intensity of the external signal and nature of the interaction of neurons.

We study numerically effects of time delay in networks of delay-coupled excitable FitzHugh-Nagumo systems with dissipation. Generation of periodic self-sustained oscillations and its threshold are analyzed depending on the dissipation of a single neuron, the delay time, and random initial conditions. The peculiarities of spatiotemporal dynamics of time-delayed bidirectional ring-structured FitzHugh-Nagumo neuronal systems are investigated in cases of local and nonlocal coupling topology between the nodes, and a first-order nonequilibrium phase transition to synchrony is established. It is shown that the emergence of an oscillatory activity in delay-coupled FitzHugh-Nagumo neurons is observed for smaller values of the coupling strength as the dissipation parameter decreases. This can provide the possibility of controlling the spatiotemporal behavior of the considered neuronal networks. The observed effects are quantified by plotting distributions of the maximal Lyapunov exponent and the global order parameter in terms of delay and coupling strength.

The work is devoted to the study of biology-relevant neural networks, which are called spiking neural networks (SNN), and is aimed at classifying two-frequency auditory signals. We consider an ensemble of FitzHugh-Nagumo neurons. Each neuron is connected to a radiophysical circuit tuned to a certain signal frequency. Different clusters of neurons respond to signals with different ratios of frequencies applied to all circuits simultaneously.

In this paper, we develop a new algorithm for estimating control parameter values of ordinary differential equation (ODE) models. We call it the complex error minimization algorithm with an adaptive rate of change. It efficiently determines the parameters of ODE models even over extremely short time series. The algorithm is based on the gradient method and successfully solves its major drawback, namely getting stuck in local minima. To detect the getting stuck, we first introduce the calculation of four different errors at once. Our studies show that they achieved the global minimum only when we observe simultaneous minimization of all these errors. When getting stuck in local minima takes place, only one (or several) errors are minimized, while the others remain unchanged or grow. Thus, the algorithm accurately detects getting stuck in local minima. After this, it applies special methods based on simulated annealing to escape from local minima. The algorithm selects the most optimal path for convergence of parameter values to the global minimum by applying random restarts and multi-start methods to avoid local minima. We have tested our method on models with regular and chaotic dynamics and have found that it can work with high accuracy in these cases. Our method is suitable for actual systems with complex dynamics and an extensive set of control parameters but short time series. Thus, the proposed algorithm is an effective method for solving the inverse problem of ODE models.

Compressive solitons arise in crystals as a result of shock loading, and they can transfer energy over long distances, exhibiting weak damping. Propagation of compressive solitons in two-dimensional (2D) materials is studied much less than in 3D crystals. Here, molecular dynamics is used to analyze the dynamics of compressive solitons in single-layer phosphorene. The mechanisms of energy dissipation by the lattice are analyzed. The results obtained are compared with those obtained earlier for graphene and boron nitride. The damping of compressive solitons in phosphorene is stronger than in graphene and boron nitride, since it has a puckered structure and, therefore, more channels for energy dissipation. Overall, our results contribute to understanding the nonlinear dynamics of localized excitations in 2D materials.

A crowdion is an interstitial atom embedded in a close-packed atomic row of a crystal lattice, it is very mobile and efficient in transferring energy and mass during plastic deformation, ion implantation, irradiation and other high-energy influences. Recently it was shown that the supersonic motion of an interstitial atom can be realized either by classical crowdion, or by a 2-crowdion, when not one, but two atoms have a high speed simultaneously. Usually static crowdions are studied using the ab initio approach, and moving excitations are modeled by the molecular dynamics method. This work presents a pioneering ab initio study of a supersonic 2-crowdion. The evolution of the electron density distribution during the motion of 2-crowdions with different supersonic speeds is analyzed. The results confirm a new mechanism of mass transfer by supersonic 2-crowdions.

Recently, much attention has been paid to the study of supersonic 2-crowdions, since they are more efficient in mass transfer in comparison with classical supersonic crowdions. A supersonic 2-crowdion requires less energy for initiation, and with the same energy as a classic crowdion, it travels a larger distance. It has been repeatedly noted that interatomic potentials affect the self-focusing propagation of 2-crowdions. It seems interesting to compare the motion of 2-crowdions in metals with different values of the stacking fault energy (SFE), since the difference in the SFE energy is one of the evidences of the difference in interatomic potentials. This paper compares the dynamics of supersonic 2-crowdions in three fcc metals, copper, nickel and aluminum, which have low, intermediate, and high SFEs, respectively. It is shown that at the same initial velocity of atoms, supersonic 2-crowdions propagate further in a metal with a lower SFE.

Crowdion presents an interstitial mobile defect propagating in close-packed crystallographic directions and plays an important role in energy and mass transfer processes occurring in bcc tungsten lattice in non-equilibrium conditions. In the present day, tungsten remains one of the most promising plasma-oriented material, which saves its protective features even under high-intensive irradiation influence in nuclear reactors. Crowdions can be one of most possible and effective nonlinear channels of energy dissipation obtaining under irradiation. The dynamics of the crowdion in the lattice with the zero or very low temperature has been already deeply studied. At the same time, influence of thermal oscillations of atoms on the crowdion dynamics has not been studied in detail, despite the processes of irradiation always occur under finite nonzero temperature. In the present work, we try to reveal changing the crowdion features under different finite temperature of the tungsten lattice.

Crowdion as one of types of an interstitial mobile defect propagating in close-packed crystallographic directions can play an important role in relaxation processes occurring in bcc lattices of tungsten in nonequilibrium conditions. The crowdions is an effectively transport of mass and energy in the metal. Tungsten is considered one of the best options as a plasma-oriented material which can be exposed to ion irradiation in nuclear reactors. Recently dynamics of crowdions has been extensively studied for different types of lattices and dimensions. However, the point of energy exchange between crowdions has not been considered earlier. The paper presents an analysis of energy exchange in a complex of crowdions located in neighboring closely packed atomic row. Obtained results reveal that closely located crowdions can intensively transfer energy from one to another thus affecting the dynamics and scenario of defect structure evolution in the crystal. It is known that irradiation of tungsten can lead to microstructural changes, such as bubbles, pores and another types of defects. Moreover, the metal constantly at these conditions are heated up to extremely high temperature. Apparently, the crowdions play an important role in the formation of different defects inside the tungsten. And aim of this work is a numerically analysis of features of the crowdion in this highly heated metal bcc lattice.

We study numerically the spatiotemporal dynamics and anti-phase synchronization of complex structures in a two-layer multiplex network of bidirectionally and repulsively coupled two-dimensional lattices. Each layer consists of locally and attractively coupled identical van der Pol oscillators. Depending on randomly distributed initial conditions the isolated layers can exhibit either a spiral or a target wave regime. The latter is found for first time for the locally coupled van der Pol lattice considered in this work. We vary the inter-layer coupling strength for either fixed or changing intra-layer coupling strengths in the interacting layers. The numerical results are summarized in the two-dimensional diagrams plotted in the "intra-layer coupling strength - inter-layer coupling strength " parameter plane. Anti-phase synchronization is identified by evaluating the local and global cross -correlation coefficients which are equal to-1. We also explore the impact of random de-multiplexing on the robustness of the observed spatiotemporal structures and anti-phase synchronized regimes in the two-layer network.