This book contains a systematic study of ecological communities of two or three interacting populations. Starting from the Lotka-Volterra system, various regulating factors are considered, such as rates of birth and death, predation and competition. The different factors can have a stabilizing or a destabilizing effect on the community, and their interplay leads to increasingly complicated behavior. Studying and understanding this path to greater dynamical complexity of ecological systems constitutes the backbone of this book. On the mathematical side, the tool of choice is the qualitative theory of dynamical systems — most importantly bifurcation theory, which describes the dependence of a system on the parameters. This approach allows one to find general patterns of behavior that are expected to be observed in ecological models. Of special interest is the reaction of a given model to disturbances of its present state, as well as to changes in the external conditions. This leads to the general idea of “dangerous boundaries” in the state and parameter space of an ecological system. The study of these boundaries allows one to analyze and predict qualitative and often sudden changes of the dynamics — a much-needed tool, given the increasing antropogenic load on the biosphere.As a spin-off from this approach, the book can be used as a guided tour of bifurcation theory from the viewpoint of application. The interested reader will find a wealth of intriguing examples of how known bifurcations occur in applications. The book can in fact be seen as bridging the gap between mathematical biology and bifurcation theory.

This first of three volumes includes papers from the second series of NODYCON, which was held virtually in February of 2021. The conference papers reflect a broad coverage of topics in nonlinear dynamics, ranging from traditional topics from established streams of research to those from relatively unexplored and emerging venues of research. These include Fluid-structure interactions Mechanical systems and structures Computational nonlinear dynamics Analytical techniques Bifurcation and dynamic instability Rotating systems Modal interactions and energy transfer Nonsmooth systems

Economic application of nonlinear dynamics, microscopic agent-based modelling, and the use of artificial intelligence techniques as learning devices of boundedly rational actors are among the most exciting interdisciplinary ventures of economic theory over the past decade. This volume provides us with a most fascinating series of examples on "complexity in action" exemplifying the scope and explanatory power of these innovative approaches.

This new approach to insect modeling discusses population dynamics' regularities, control theory, theory of transitions, and describes methods of population dynamics and outbreaks modeling for forest phyllophagous insects and their effects on global climate change. Research in insect population dynamics is important for more reasons than just protecting forest communities. Insect populations are among the main ecological units included in the analysis of stability of ecological systems. Moreover, it is convenient to test new methods of analyzing population and community stability on the insect-related data, as by now ecologists and entomologists have accumulated large amounts of such data. In this book, the authors analyze population dynamics of quite a narrow group of insects – forest defoliators. It is hoped that the methods proposed herein for the analysis of population dynamics of these species may be useful and effective for analyzing population dynamics of other animal species and their effects and role in global warming. What can insects tell us about our environment and our ever-changing climate? It is through studies like this one that these important answers can be obtained, along with data on the insects and their behaviors themselves. The authors present new theories on modeling and data accumulation, using cutting-edge processes never before published for such a wide audience. This volume presents the state-of-the-art in the science, and it is an essential piece of any entomologist's and forest engineer's library.

This book is a collection of papers devoted to the emergence and development in Bulgarian Academy of Sciences of some of the areas of informatics, including artificial intelligence. The papers are prepared by specialists from the Academy, some of whom are among the founders of these scientific and application areas in Bulgaria and in some cases – in the world. The book is interesting for specialists in informatics and computer science and researchers in history of sciences.

Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. his fourth volume concentrates on reviewing further relevant contemporary applications of chaotic and nonlinear dynamics as they apply to the various cuttingedge branches of science and engineering. This encompasses, but is not limited to, topics such as synchronization in complex networks and chaotic circuits, time series analysis, ecological and biological patterns, stochastic control theory and vibrations in mechanical systems. Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘recipe book’ full of tried and tested, successful engineering applications.

Contains both an exhaustive introduction to the subject as well as a detailed discussion of fundamental problems and research results. Despite the unified presentation of the subject, care has been taken to present the material in largely self-contained chapters.

The contributed volume puts emphasis on a superior role of water in (bio)systems exposed to a mechanical stimulus. It is well known that water plays an extraordinary role in our life. It feeds mammalian or other organism after distributing over its whole volume to support certain physiological and locomotive (friction-adhesion) processes to mention but two of them, both of extreme relevance. Water content, not only in the mammalian organism but also in other biosystems such as whether those of soil which is equipped with microbiome or the ones pertinent to plants, having their own natural network of water vessels, is always subjected to a force field.The decisive force field applied to the biosystems makes them biomechanically agitated irrespective of whether they are subjected to external or internal force-field conditions. It ought to be noted that the decisive mechanical factor shows up in a close relation with the space-and-time scale in which it is causing certain specific phenomena to occur.The scale problem, emphasizing the range of action of gravitational force, thus the millimeter or bigger force vs. distance scale, is supposed to enter the so-called macroscale approach to water transportation through soil or plants’ roots system. It is merely related to a percolation problem, which assumes to properly inspect the random network architecture assigned to the biosystems invoked. The capillarity conditions turn out to be of prior importance, and the porous-medium effect has to be treated, and solved in a fairly approximate way.The deeper the scale is penetrated by a force-exerting and hydrated agent the more non-gravitational force fields manifest. This can be envisaged in terms of the corresponding thermodynamic (non-Newtonian) forces, and the phenomena of interest are mostly attributed to suitable changes of the osmotic pressure. In low Reynolds number conditions, thus in the (sub)micrometer distance-scale zone, they are related with the corresponding viscosity changes of the aqueous, e.g. cytoplasmatic solutions, of semi-diluted and concentrated (but also electrolytic) characteristics. For example, they can be observed in articulating systems of mammals, in their skin, and to some extent, in other living beings, such as lizards, geckos or even insects. Through their articulating devices an external mechanical stimulus is transmitted from macro- to nanoscale, wherein the corresponding osmotic-pressure conditions apply. The content of the proposed work can be distributed twofold. First, the biomechanical mammalian-type (or, similar) systems with extraordinary relevance of water for their functioning will be presented, also including a presentation of water itself as a key physicochemical system/medium. Second, the suitably chosen related systems, mainly of soil and plant addressing provenience, will be examined thoroughly. As a common denominator of all of them, it is proposed to look at their hydrophobic and/or (de)hydration effects, and how do they impact on their basic mechanical (and related, such as chemo-mechanical or piezoelectric, etc.) properties. An additional tacit assumption employed throughout the monograph concerns statistical scalability of the presented biosystems which is equivalent to take for granted a certain similarity between local and global system’s properties, mostly those of mechanical nature. The presented work’s chapters also focus on biodiversity and ecological aspects in the world of animals and plants, and the related systems. The chapters’ contents underscore the bioinspiration as the key landmark of the proposed monograph.

The dynamics of physical, chemical, biological, or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. This book is a comprehensive introduction to this field, suited to a broad readership, and reflecting a wide range of applications. Some of the concepts considered are: topological equivalence; embeddings; dimensions and fractals; Poincaré maps and map-dynamics; empirical computational sciences vis-á-vis mathematics; Ulam's synergetics; Turing's instability and dissipative structures; chaos; dynamic entropies; Lorenz and Rossler models; predator-prey and replicator models; FPU and KAM phenomena; solitons and nonsolitons; coupled maps and pattern dynamics; cellular automata.