Nikolay Vladimirovich Kuznetsov

• PhD
• Head of Department at St Petersburg University

https://dergipark.org.tr/en/pub/chaos/issue/86422

https://dergipark.org.tr/en/pub/chaos/issue/83761

https://dergipark.org.tr/en/pub/chaos/issue/80150

https://dergipark.org.tr/en/pub/chaos/issue/77246

Within the framework of the development of the theory of hidden oscillations, the problem of determining the boundary of global stability and revealing its hidden parts corresponding to the non-local birth of hidden oscillations is considered. For a phase-locked loop with a proportional-integrating filter and a piecewise-linear phase detector chara...

Eleven years have passed since the discovery of the first chaotic hidden attractor in Chua system with piecewise-linear nonlinearity. Experimental observation of such attractor is still a hard work as the attraction basin of such hidden attractor does not intersect with any system equilibrium point and is far away from the origin. The key technical...

https://dergipark.org.tr/en/pub/chaos/issue/75756

https://dergipark.org.tr/en/pub/chaos/issue/73767

After the discovery in early 1960s by E. Lorenz and Y. Ueda of the first example of a chaotic attractor in numerical simulation of a real physical process, a new scientific direction of analysis of chaotic behavior in dynamical systems arose. Despite the key role of this first discovery, later on a number of works have appeared supposing that chaot...

The paper is devoted to the problem of spacecraft attitude control using reaction wheels. The control system should ensure switching between less accurate to more accurate flight modes, resistance to external environmental influences, and, in some cases, the survival of the spacecraft. In these modes, the reaction wheel drives can reach their maxim...

https://dergipark.org.tr/en/pub/chaos/issue/73033

The paper is devoted to a human operator control for an electromechanical remote manipulator. It is assumed that a human operator in a closed-loop achieves the goal of control by deflecting the joystick. A saturation nonlinearity is taken into account in the paper. To compensate for the negative phase delay in the system performance, a corrective f...

This paper deals with computer-controlled pneumatic actuators for the Gough-Stewart platform with 6 degrees of freedom. An important feature considered in the paper pneumatic actuator is the use of a group of valves rather than a spool valve to control the pressure in the chambers, which leads to a significant quantization in terms of the level of...

The purpose of this work is to demonstrate the application of the nonlinear correction method to prevent attitude oscillations of flying vehicles. This paper investigates the complications of manual control tasks in aeronautics caused by employing the integral component in the control loop. If the actuators of aircraft controlling surfaces reach th...

In the field of complex dynamics, multistable attractors have been gaining significant attention due to their unpredictability in occurrence and extreme sensitivity to initial conditions. Co-existing attractors are abundant in diverse systems ranging from climate to finance and ecological to social systems. In this article, we investigate a data-dr...

The development of automation technologies in various fields of human life poses the problem of studying human-machine systems interaction and the influence of human on machine actions. The varied human behavior and the complexity of his central nervous system organization are a disability to his mathematical description. However, despite this, the...

In the field of complex dynamics, multistable attractors have been gaining a significant attention due to its unpredictability in occurrence and extreme sensitivity to initial conditions. Co-existing attractors are abundant in diverse systems ranging from climate to finance, ecological to social systems. In this article, we investigate a data-drive...

In the present work, a second-order type-2 phase-locked loop (PLL) with a piecewise-linear phase detector characteristic is analyzed. An exact solution to the Gardner problem on the lock-in range is obtained for the considered model. The solution is based on a study of cycle slipping bifurcation, which improves the well-known engineering estimates.

This issue is dedicated to the memory of Prof. Tenreiro Machado. https://dergipark.org.tr/en/pub/chaos/issue/64884

Irregular, especially chaotic, behavior is often undesirable for economic processes because it presents challenges for predicting their dynamics. In this situation, control of such a process by its mathematical model can be used to suppress chaotic behavior and to transit the system from irregular to regular dynamics. In this paper, we have constru...

The obituary of Professor Arkadii Gelig, who passed away on October 6, 2021. The English translation is provided as linked data.

The dynamical system without equilibrium point is considered having hidden dynamics. It is relatively difficult to locate the attractor in the state space as its attraction basin has nothing to do with the equilibrium point. Especially, generation of multi-scroll chaos from no-equilibrium system is a challenging task. In this paper, using sine func...

Chaos Theory and Applications (March 2022 - Volume 4 - Issue 1) https://dergipark.org.tr/en/pub/chaos/issue/63571 ----------- 1) Jun MA. "Chaos Theory and Applications：The Physical Evidence, Mechanism are Important in Chaotic Systems. " 2) Burak ARICIOĞLU, Sezgin KAÇAR. "Circuit Implementation and PRNG Applications of Time Delayed Lorenz System....

This paper deals with defining the concept of agent‐based time delay margin and computing its value in multi‐agent systems controlled by event‐triggered based controllers. The agent‐based time delay margin specifying the time delay tolerance of each agent for ensuring consensus in event‐triggered controlled multi‐agent systems can be considered as...

Phase-Locked Loops (PLL) may be included into modern MEMS gyroscopes to provide excitation of inertial mass oscillations, as well as to form clock signal for digital signal processing in an integrated circuit. This paper considers the impact of PLL architecture on MEMS gyroscope performance and its estimation. It is shown that the proposed Double S...

Fibonacci-like polynomials, the roots of which are responsible for a cyclic behavior of orbits of a second-order two-parametric difference equation, are considered. Using Maple and Wolfram Alpha, the location of the largest and the smallest roots responsible for the cycles of period p among the roots responsible for the cycles of periods 2kp (perio...

The influence of higher nervous activity on the processes of autonomic control of the cardiovascular system and baroreflex regulation is of considerable interest, both for understanding the fundamental laws of the functioning of the human body and for developing methods for diagnostics and treatment of pathologies. The complexity of the analyzed sy...

In this paper, the D3 dihedral logistic map of fractional order is introduced. The map presents a dihedral symmetry D3. It is numerically shown that the construction and interpretation of the bifurcation diagram versus the fractional order requires special attention. The system stability is determined and the problem of hidden attractors is analyze...

In this chapter, the issues of global stability, bifurcations, and emergence of nontrivial limiting dynamic regimes in systems described by differential equations with discontinuous right-hand sides are considered within the framework of the theory of hidden oscillations. Such systems are important in the problems of mechanics, engineering, and con...

The talk is devoted to research and suppression of hidden oscillations in manned aircraft flight altitude control. Active action from the pilot during landing can lead to saturation in the speed of the steering surface drive, and due to the erroneous reaction of the pilot, cause the appearance of hidden oscillations of the aircraft (the so-called p...

This work is devoted to the study of the possibility of the appearance and localization of hidden vibrations in the system of adaptive suppression of the flexural-torsional flutter of the wing. The control algorithm, built in the form of a modified adaptive controller with an implicit reference model, uses measurements of the wing torsion angle and...

In the paper, a digital control law for adaptive suppression of the flexural-torsional wing flutter has been developed and analyzed. The control law uses measurements of the wing twist angle (“angle of attack”) and its time derivative. The implicit reference model (IRM) method was used for the synthesis of the so-called “simple adaptive controller”...

In this paper, the closed-loop human-machine system is studied under the framework of the control systems theory. The human operator model is considered concerning the human's ability for adaptation to the current operational conditions. For flying vehicles this property corresponds the crossover model by McRuer. In the paper, the actuator is model...

In this paper the D 3 dihedral logistic map of fractional order is introduced. The map 1 presents a dihedral symmetry D 3 . It is numerically shown that the construction and interpretation 2 of the bifurcation diagram versus the fractional order require special attention. The system stability 3 is determined and the problem of hidden attractors is...

In the present work, a second-order PLL with lead-lag loop filter and triangular phase detector characteristic is analysed. An exact value of the conservative lock-in range is obtained for the considered model. The solution is based on analytical integration of the considered model on the linear segments.

In the present work, a second-order type 2 PLL with a piecewise-linear phase detector characteristic is analysed. An exact solution to the Gardner problem on the lock-in range is obtained for the considered model. The solution is based on a study of cycle slipping bifurcation and improves well-known engineering estimates.

The paper focuses on a manned aircraft landing control system. It is known that actuator level and rate limitations can cause pilot-induced oscillations. This phenomenon occurs during intensive pilot control in a closed-loop system under certain initiating conditions associated with both the influence of the external environment and changes in the...

In the modern educational process aimed on preparing professionals in the applied areas, it’s crucial, along with purely professional training, to provide students both with solid theoretical background and help them to develop “soft skills” that will facilitate their smooth and efficient adaptation to the industry realities when they start their p...

This letter deals with a novel variant of antithetic integral feedback controller (AIFC) motifs which can feature robust perfect adaptation, a pervasive (desired) ability in natural (synthetic) biomolecular circuits, when coupled with a wide class of process networks to be regulated. Using the separation of timescales in the proposed kind of AIFC,...

Chaos Theory and Applications (November 2021 - Volume 3 - Issue 2) https://dergipark.org.tr/en/pub/chaos/issue/58077

Cyclicality and instability inherent in the economy can manifest themselves in irregular fluctuations, including chaotic ones, which significantly reduces the accuracy of forecasting the dynamics of the economic system in the long run. We focus on an approach, associated with the identification of a deterministic endogenous mechanism of irregular f...

This paper studies a system of coupled discrete fractional-order logistic maps, modeled by Caputo’s delta fractional difference, regarding its numerical integration and chaotic dynamics. Some interesting new dynamical properties and unusual phenomena from this coupled chaotic-map system are revealed. Moreover, the coexistence of attractors, a neces...

The aim of this report is to investigate an adaptive synchronization (AS) for the general class of complex hyperchaotic models with unknown parameters and a new algorithm to achieve this type of synchronization is proposed. Owing to the intricacy behavior of hyperchaotic models that could be effective in secure communications, the special control b...

In this paper a fairly complete mathematical model of CP-PLL, which reliable enough to serve as a tool for credible analysis of dynamical properties of these circuits, is studied. We refine relevant mathematical definitions of the hold-in and pull-in ranges related to the local and global stability. Stability analysis of the steady state for the ch...

The first mathematical problems of the global analysis of dynamical models can be traced back to the engineering problem of the Watt governor design. Engineering requirements and corresponding mathematical problems led to the fundamental discoveries in the global stability theory. Boundaries of global stability in the space of parameters are limite...

Cyclicity and instability inherent in the economy can manifest themselves in irregular fluctuations, including chaotic ones, which significantly reduces the accuracy of forecasting the dynamics of the economic system in the long run. We focus on an approach, associated with the identification of a deterministic endogenous mechanism of irregular flu...

This work presents the continuation of the recent article ''The Lorenz system: hidden boundary of practical stability and the Lyapunov dimension'', published in the Nonlinear Dynamics journal. In this work, in comparison with the results for classical real-valued Lorenz system (henceforward -- Lorenz system), the problem of analytical and numerical...

This report aims to study adaptive synchronization between a general class of hyperchaotic complex-valued systems with unknown parameters, which is motivated by extensive application areas of this topic in nonlinear sciences (e.g., secure communications, encryption techniques, etc.). Based on the complexity of hyperchaotic dynamical systems, which...

This paper presents an effective approach to constructing numerical attractors of a general class of continuous homogenous dynamical systems: decomposing an attractor as a convex combination of a set of other existing attractors. For this purpose, the convergent Parameter Switching (PS) numerical method is used to integrate the underlying dynamical...

Dynamics of the New Keynesian model in continuous time with the Rotemberg pricing mechanism is considered within a framework of an optimal control problem. Various regimes of monetary and fiscal policy (‘active’ and ‘passive’) can lead to unstable dynamics in the economy. Parameters of the Taylor rules for both monetary and fiscal policies determin...

Gennady Alekseevich Leonov (1947 – 2018) – Corresponding member of the Russian Academy of Sciences, Foreign Member of the Finnish Academy of Science and Letters, a Council Member of International Federation of Automatic Control, the Highly Cited Mathematician of the Russian Federation, a bearer of many notable awards – passed away on April 23, 2018...

This paper discusses one of the approaches to analysis of the global stability boundaries of type 2 PLLs.

The paper discusses one of the issues of interaction of inverter electrical systems with control systems based on special models of the phase-locked loop, called Enhanced Phase-Locked Loop.

Analysis of the phase space of discontinuous systems via classical methods of the theory of oscillations can be quite a difficult task. Moreover, in some cases this analysis is impossible to perform. Due to the emergence of frequency methods for analysis of discontinuous systems and the development of various analytical-numerical methods, it has be...

Methods of nonlinear analysis and synthesis of synchronization control systems for electrical grids have been developed. The use of averaging methods and Lyapunov-type stability criteria for the cylindrical phase space have made it possible for the first time in the Gardner problem to obtain analytical estimates of the system parameters to ensure a...

Synchronization of fractional-order hyperchaotic complex systems is an interesting phenomenon since it has several applications in applied sciences. Based on the complexity of hyperchaotic dynamical systems and unpredictability of hidden attractors, which may exist in their phase spaces and could be beneficial in secure communications, a scheme to...

We have identified the chimera states in a class of non-locally coupled network of hidden oscillators without equilibrium, with one and two stable equilibria. All these cases exhibit hidden chaotic oscillations when isolated. We show that the choice of initial conditions is crucial to observe chimeras in these hidden oscillatory networks. The obser...

In this paper, it is found numerically that the previously found hidden chaotic attractors of the Rabinovich–Fabrikant system actually present the characteristics of strange nonchaotic attractors. For a range of the bifurcation parameter, the hidden attractor is manifestly fractal with aperiodic dynamics, and even the finite-time largest Lyapunov e...

This work is devoted to the analysis of a mathematical model of hydropower unit, consisting of synchronous generator, hydraulic turbine, and speed governor. It is motivated by the accident happened on the Sayano-Shushenskaya hydropower plant in 2009. In the analysis we follow the line of classical mathematical control theory approach developed in t...

The first hidden chaotic attractor was discovered in a dimensionless piecewise-linear Chua’s system with a special Chua’s diode. But designing such physical Chua’s circuit is a challenging task due to the distinct slopes of Chua’s diode. In this paper, a modified Chua’s circuit is implemented using a 5-segment piecewise-linear Chua’s diode. In part...

In the present chapter various approaches to estimate the fractal dimension and the Hausdorff dimension, which involve Lyapunov functions, are developed. One of the main results of this chapter is a theorem called by us the limit theorem for the Hausdorff measure of a compact set under differentiable maps. One of the sections of Chap. 5 is devoted...

In Chap. 2 the dimension of a vector space was defined as the maximal number of linearly independent vectors existing in it. The simplest example of an n-dimensional space, whose dimension is understood in this sense, is the space \(\mathbb R^n\). The dimension theory, which was developed in the early 20th century, has extended this conception to m...

Nowadays there is a number of surveys and theoretical works devoted to Lyapunov exponents and Lyapunov dimension, however most of them are devoted to infinite dimensional systems or rely on special ergodic properties of a system. At the same time the provided illustrative examples are often finite dimensional systems and the rigorous proof of their...

In this chapter we derive dimension and entropy estimates for invariant sets and global \(\mathcal{B}\)-attractors of cocycles in non-fibered and fibered spaces. A version of the Douady-Oesterlé theorem will be proven for local cocycles in an Euclidean space and for cocycles on Riemannian manifolds. As examples we consider cocycles, generated by th...

Global stability and dimension properties of nonlinear differential equations essentially depend on the contraction properties of k-parallelopipeds or k-ellipsoids under the flow of the associated variational equations. The goal of this second chapter is to develop some elements of multilinear algebra for the investigation of linear differential eq...

In this chapter dimension estimates for maps and dynamical systems with specific properties are derived. In Sect. 10.1 a class of non-injective smooth maps is considered. Dimension estimates for piecewise non-injective maps are given in Sect. 10.2. For piecewise smooth maps with a special singularity set upper Hausdorff dimension estimates are show...

In this chapter generalizations of the Douady-Oesterlé theorem (Theorem 5.1, Chap. 5) are obtained for maps and vector fields on Riemannian manifolds. The proof of the generalized Douady-Oesterlé theorem on manifolds is given in Sect. 8.1. In Sect. 8.2 it is shown that the Lyapunov dimension is an upper bound for the Hausdorff dimension. A tubular...

The main tool in estimating dimensions of invariant sets and entropies of dynamical systems developed in this book is based on Lyapunov functions. In this chapter we introduce the basic concept of global attractors. The existence of a global attractor for a dynamical system follows from the dissipativity of the system. In order to show the last pro...

The first part (Sects. 4.2, 4.3, 4.5 and 4.6) of the present chapter contains several approaches to the investigation of the Fourier spectrum of almost periodic solutions to various differential equations. The core element here is the Cartwright theorem [6] that links the topological dimension of the orbit closure of an almost periodic flow and the...

In this chapter we present some auxiliary results from the linear operator theory and stability theory which are used in the sequel for dimension estimation. In Sect. 7.1 some elements of the exterior calculus of linear operators in linear spaces are introduced. Section 7.2 is concerned with orbital stability results for vector fields on Riemannian...

This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carathéodory dimensions) for attractors and invariant sets of dynamical systems and cocycles generated by smooth differential equations or maps in finite-dimensional Euclidean spaces or on manifolds. It also discusses stability i...

The development of electric aircraft, the design of which will use, apart from doing away with pneumatic and hydraulic transmissions, electric propulsion, is one of promising lines in aviation technology. As an example, the project of the X-57 Maxwell electric aircraft developed by NASA, which is equipped with 14 propulsion electric motors, is give...

Irregular fluctuations in economy lead to unpredictable effects and disrupt its stable functioning. Various tools could be used to stabilize irregular dynamics in economic models. For example, to introduce control into the model as an external function, as well as to take into account the internal characteristics of economic agents in the economy u...

This book presents a collection of new articles written by world-leading experts and active researchers to present their recent finding and progress in the new area of chaotic systems and dynamics, regarding emerging subjects of unconventional chaotic systems and their complex dynamics.It guide readers directly to the research front of the new scie...

Phase-locked loop is classical nonlinear control system for frequency and phase synchronization in electrical circuits. According to the Egan conjecture, the type 2 loops have an infinitely large pull-in range. This article reconsider the pull-in problem for the fourth order type 2 PLLs. The global stability domain is estimated by applying Lyapunov...

Depending on the flight mode, the airflow can either damp aircraft oscillations, or, conversely, the oscillating structure takes energy from the incoming flow, as a result of which a rapid increase in amplitude of oscillations may occur. This dangerous phenomenon has become a significant obstacle to the development of high-speed aviation. Since the...

In this article, we construct a kind of three-dimensional piecewise linear (PWL) system with three switching manifolds and obtain four theorems with regard to the existence of a homoclinic orbit and a heteroclinic cycle in this class of PWL system. The first theorem studies the existence of a heteroclinic cycle connecting two saddle-foci. The exist...

In 1981, famous engineer William F. Egan conjectured that a higher-order type 2 PLL with an infinite hold-in range also has an infinite pull-in range, and supported his conjecture with some third-order PLL implementations. Although it is known that for the second-order type 2 PLLs the hold-in range and the pull-in range are both infinite, the prese...

Asymmetric self-excited periodic motions or periodic solutions that are produced by relay feedback system that have symmetric characteristics are studied in the paper. Two different mechanisms of producing an asymmetric oscillation by a system with symmetric properties are noted and analyzed by the locus of a perturbed relay system (LPRS) method. B...

Counter-examples to Aizerman's and Kalman's conjectures are considered. Investigation of the behavior in the vicinity of the origin and at a distance from the origin is done. The simultaneous existence of both: a limit cycle and asymptotic or finite-time convergence is proved through the LPRS method and the Lyapunov method, respectively. Conclusion...

On the example of the famous Lorenz system, the difficulties and opportunities of reliable numerical analysis of chaotic dynamical systems are discussed in this article. For the Lorenz system, the boundaries of global stability are estimated and the difficulties of numerically studying the birth of self-excited and hidden attractors, caused by the...

Forecasting and analyses of the dynamics of financial and economic processes such as deviations of macroeconomic aggregates (GDP, unemployment, and inflation) from their long-term trends, asset markets volatility, etc., are challenging because of the complexity of these processes. Important related research questions include, first, how to determin...

The development of the theory of absolute stability, the theory of bifurcations, the theory of chaos, theory of robust control, and new computing technologies has made it possible to take a fresh look at a number of well-known theoretical and practical problems in the analysis of multidimensional control systems, which led to the emergence of the t...

In this article using an analytical method called Fishing principle we obtain the region of parameters, where the existence of a homoclinic orbit to a zero saddle equilibrium in the Lorenz-like system is proved. For a qualitative description of the different types of homoclinic bifurcations, a numerical analysis of the obtained region of parameters...

Roll angular motion of the modern aircraft operating in non-linear flight modes with a high angle of attack often demonstrates the limit cycle oscillations, which is commonly known as the wing rock phenomenon. Wing rock dynamics are represented by a substantially non-linear model, with parameters varying over a wide range, depending on the flight c...