The effect of small internal and dashpot damping on a trapped mode of a 1D-waveguide, that is, a semi-infinite string on a Winkler elastic foundation, has been investigated. At the edge of the string a mass-spring-damper system is attached. The string is assumed to have an internal damping. Four models for the internal damping are considered: air damping, Kelvin-Voigt damping, local Kelvin-Voigt damping, and damping related to time hysteresis. Depending on the internal damping and the parameters in the formulated problem, it will be shown that the amplitude of a trapped mode of the string can decrease or increase with time.

We consider systems of reaction–diffusion equations. We describe a new effect in the wave interaction for these systems: the collision of several travelling fronts may induce chaos or periodic oscillations. This effect depends on the initial locations of the travelling fronts: For some initial positions chaos occurs and for others it does not. In a space-homogeneous system, we need at least three fronts to create time-periodic behaviour, while to create chaos, we should have four fronts. We also provide a short review of previously known results, and different known mechanisms of chaos generation for reaction–diffusion systems. Our results can be used for pattern coding, in particular, for morphogenesis.

We analyze a category of slow-fast dynamical systems that exhibit complex bifurcations as the dynamic parameter, representing the load on the system, undergoes variation. We establish that within such systems featuring distinct structurally stable dynamical states, a transition from the first regime to the second ensues as a consequence of load variation. We extend these concepts to investigate bifurcations in conceptual climate models, specifically those resulting from restrictions on greenhouse gas emissions.

Exposure of cells to non‐optimal growth conditions or to any environment that reduces cell viability can be considered as a stress. In this paper, we are going to highlight the main factors that determine the danger of stress to a cell considered as a biochemical system. To this end, we introduce a new mathematical concept of biosystem stability, where we take into account a signal transduction by deep gene networks. Using this concept and known results on approximations by deep networks, we find asymptotic estimates of the size and the depth of gene regulation networks that define the stress response. We propose a new algorithm to find the gene network approximating a prescribed output. It allows us, with the help of Kolmogorov ‐entropy and the deep neural network theory, to estimate the number of genes involved in regulation of responses on a stress (for example, a heat shock). We show that the main factors that increase the sensitivity of the systems with respect to a stress are the number of biochemical network parameters affected by the stress and sensitivities of kinetic rates with respect to these parameters.

This manuscript introduces a novel spin model that captures the dynamics of ecological systems. We assume that these ecosystems consist of species whose ecological properties are completely determined by their discrete genotypes, and these genotypes are encoded by spin strings. We demonstrate that the Hamiltonian of this spin model can be derived naturally from classical models of population dynamics. Specifically, we establish a connection between the maximization of species abundance and the minimization of the Hamiltonian. The standard mean-field analysis reveals that the proposed spin model corresponds to the well-known Hopfield system, in general, characterized by asymmetric interactions. Remarkably, the resulting Hopfield system can possess an exponential number of local attractors, which, in the case of asymmetric interactions, may be complex. We term this characteristic “super multistationarity”. We also demonstrate that super multistationarity combined with spontaneous symmetry breaking empowers populations to identify optimal genotypes. This adaptation process mirrors the search for solutions in a parallel computer.

In this paper, the dynamics of a compressed Euler-Bernoulli beam on a Winkler elastic foundation under the action of an external nonlinear force, which models a wind force, is studied. The beam is assumed to be long, and the lower part of its spectrum is prescribed. An asymptotic method is proposed to find the parameters of the beam, in order to have this prescribed lower part of the spectrum. All these parameters are necessary to guarantee the stability of the beam and to avoid resonances between the low frequency modes. These modes have special spatial supports that exclude a direct interaction between them. It is shown that the Galerkin system describing the time evolution can be decomposed into a system of almost independent equations which describes n independent nonlinear oscillators. Each oscillator has its own phase and frequency. It is shown that interaction between oscillators can exist only through high frequency modes.

This manuscript presents an algorithmic approach to cooperation in biological systems, drawing on fundamental ideas from statistical mechanics and probability theory. Fisher’s geometric model of adaptation suggests that the evolution of organisms well adapted to multiple constraints comes at a significant complexity cost. By utilizing combinatorial models of fitness, we demonstrate that the probability of adapting to all constraints decreases exponentially with the number of constraints, thereby generalizing Fisher’s result. Our main focus is understanding how cooperation can overcome this adaptivity barrier. Through these combinatorial models, we demonstrate that when an organism needs to adapt to a multitude of environmental variables, division of labor emerges as the only viable evolutionary strategy.

Permafrost thaw reinforces greenhouse gas production. The resulting growth of greenhouse gases (especially methane) in the atmosphere may trigger a climate system bifurcation. To study how changes in the microbial community may cause greenhouse gas emissions from permafrost and produce bifurcations in climate temperature dynamics we propose a conceptual nonlinear model that couples an atmospheric dynamics model with the population structure of microbial communities. Our model is mathematically well-posed, demonstrating that microbial population diversity can significantly lower planetary surface temperatures, an outcome contingent upon the average population parameters and their standard deviations.

Excitable media are prevalent models for describing interesting effects in physical, chemical, and biological systems such as pattern formation, chaos, and wave propagation. In this manuscript, we propose a spatially extended variant of the FitzHugh–Nagumo model that exhibits new effects. In this excitable medium, waves of new kinds propagate. We show that the time evolution of the medium state at the wavefronts is determined by complicated attractors which can be chaotic. The dimension of these attractors can be large and we can control the attractor structure by initial data and a few parameters. These waves are capable transfer complicated information given by a Turing machine or associative memory. We show that these waves are capable to perform cell differentiation creating complicated patterns.

This article considers the formation of a new ESG agenda under the conditions of the spring sanctions. In particular, an attempt has been made to answer the following questions: to what extent will changes in the geopolitical situation at the global level affect the ecological transformation of both the national economy of the Russian Federation and within regional international organizations? What will be the main formats of ESG - agenda realization on the international level? What are the prerequisites for ESG-concept implementation in Russian business community? The article contains analytical review of prerequisites and catalyst factors for the formation of a new model of development of ecologization of economy. It is established that as a result of the process of de-globalization of the world economy, the imposition of sanctions against Russia, the main vector of development of environmental initiatives remains the regional format of international integration organizations based on the principles of import substitution, digitalization, multivariate, comprehensiveness and quality. As a result of the study the potential shape of the paradigm of ESG agenda implementation in the medium term at the national and regional level is formulated.

This paper aims to explain the transition to multicellularity as a consequence of the evolutionary response to stress. The proposed model is composed of three parts. The first part details stochastic biochemical kinetics within a reactor (potentially compartmentalized), where kinetic rates are influenced by random stress parameters, such as temperature, toxins, oxidants, etc. The second part of the model is a feedback mechanism governed by a genetic regulation network (GRN). The third component involves stochastic dynamics that describe the evolution of this network. We assume that the organism remains viable as long as the concentrations of certain key reagents are maintained within a defined range (the homeostasis domain). For this model, we calculate the probability estimate that the system will stay within the homeostasis domain under stress impacts. Under certain assumptions, we show that a GRN expansion increases the viability probability in a very sharp manner. It is shown that multicellular organisms increase their viability due to compartment organization and stem cell activity. By the viability probability estimates, an explanation of the Peto paradox is proposed: why large organisms are stable with respect to cancer attacks.

A new semi-empirical model is presented for the vortex-induced vibration of structures. The lift force on a structure is assumed to consist of two components. The first component is a non-linear force that has a polynomial dependence on the velocity of the structure. The second component is a harmonic force with the Strouhal frequency. Only the crossflow motion of the structure is considered. The maximum response amplitude of the structure is estimated as well as the phase difference between the structural displacement and the periodic component of the lift force. The model predictions are compared with experimental results available in literature to show good qualitative agreement.

The article deals with the impact of the current socio-economic situation caused by the introduction of international sanctions and the cessation of transnational cooperation in many areas, including transport and logistics ecosystems. At the same time, the task of ecologization of the transport industry and its sustainable development is urgent for each state. Within the framework of existing strategies for the development of national transport complexes, a set of measures aimed at implementing the concept of sustainable transport is being implemented.

This research illustrates that complex dynamics of gene products enable the creation of any prescribed cellular differentiation patterns. These complex dynamics can take the form of chaotic, stochastic, or noisy chaotic dynamics. Based on this outcome and previous research, it is established that a generic open chemical reactor can generate an exceptionally large number of different cellular patterns. The mechanism of pattern generation is robust under perturbations and it is based on a combination of Turing's machines, Turing instability and L. Wolpert's gradients. These results can help us to explain the formidable adaptive capacities of biochemical systems.

Critical phenomena in the climate system can cause drastic changes in the state of plan-etary ecosystems as well the entire biosphere. There also are mechanisms through which the biosphere can make an effect on climate. In this manuscript, we study the nonlinear dynamics of the interaction of the climate system with the biosphere by linking an energy balance climate model to different species competition models. We develop an asymptotic approach to these models and investigate how migration strengthens biome stability and biodiversity. Moreover, we derive relations describing biome boundary shifts under global warming (or cooling) and check those relations against paleo data on plant biome loca-tion. Finally, the models demonstrate that critical rates of changes in the environmental temperature dynamics may shift biome stability.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

Considering the limited pace of development and opportunities for modernization of existing conventional transport systems, the article analyzes effective solutions to problems of the existing transport system of the Russian Federation, in which a radical increase in the speed and capacity of transport lines, combined with acceptable cost and low energy consumption for the movement of passengers and goods, is possible. Traditional and innovative transport technologies are compared on the basis of speed, energy and transport efficiency criteria. The considered large-scale project of creation of the Integrated Transit Transport System on the basis of the vacuum magnetolevitational transport technology is an example of convergence of magnetolevitational, superconducting and vacuum technologies for land transport allowing achieving hypersonic speeds with high throughput capacity of the main line and record low energy costs due to the emerging possibility of maximum degree of energy recuperation of traffic.

In this paper, we consider reaction-diffusion systems, which describe the propagation of waves with chaotic and time periodic fronts. Using this property, we show that there exist reaction-diffusion models with a few of reagents, which, by a variation of initial data, is capable to generate all possible one-dimensional cell patterns. We describe algorithms, which allow to obtain any prescribed target cell patterns by chaotic waves. Our model can be considered as a reaction-diffusion analogue of universal Turing machine. So, we propose a new robust mechanism of positional information transfer, which, in contrast to Wolpert' gradients, can work at long distances. Universality of our model helps to explain why genes, responsible for morphogenesis, are highly conservative within long evolution periods.

In this paper the dynamics of a weakly nonlinear elastic string on a Winkler elastic foundation is studied. The foundation may be spatially heterogeneous. At one end of the string a mass-spring system is attached, and the other end of the string is fixed. The string is assumed to be long, and the lower part of the spectrum of the string is prescribed. It is shown that localized modes exist and that the dynamics of the string for large times is determined by these localized modes. The frequencies of these localized modes can be controlled by special choices for the spatial heterogeneities in the elastic foundation. Analytical and numerical results are presented to illustrate the findings.