experiments on node to node pinning control of chua s circuits abstract in this paper we study the global intermittent pinning controllability of networks of coupled chaotic oscillators we explore the feasibility of the recently presented node to node pinning control strategy through experiments on chua s circuits we focus on the case of two peer to peer coupled chua s circuits and we build a novel test bed platform comprised of three inductorless chua s oscillators we investigate the effect of a variety of design parameters on synchronization performance including the coupling strength between the oscillators the control gains and the switching frequency of node to node pinning control experimental results demonstrate the effectiveness of this novel pinning control strategy in rapidly taming chaotic oscillator dynamics onto desired reference trajectories while minimizing the overall control effort and the number of pinned network sites from an analytical standpoint we present sufficient conditions for global node to node pinning controllability and we estimate the maximum switching period for network controllability by adapting and integrating available results on lyapunov stability theory and partial averaging techniques

birth and death of the double scroll abstract the double scroll is a chaotic attractor observed from an extremely simple electronic circuit made of 4 linear circuit elements 2 capacitors 1 inductor and 1 resistor and a 2 terminal nonlinear resistor characterized by a 3 segment piecewise linear v i characteristic this nonlinear resistor can be built in the laboratory using 2 transistors and diodes the qualitative behavior of the double scroll attractor has been described elsewhere where each cross section of the double scroll attractor is shown to consist of 2 tightly wound spirals our objective in this paper is to present a bifurcation analysis of this circuit in terms of 2 basic parameters various bifurcation phenomena such as hopf bifurcation period doubling cascades rossler s spiral and screw type attractors periodic windows shilnikov phenomenon double scroll and boundary crisis are described in particular special emphasis is given to the mechanisms leading to the birth and the death of the double scroll attractor all bifurcation phenomena described in this paper are observed not only experimentally but also confirmed by digital computer simulations moreover an analytical foundation of the double scroll family of equations has been developed and used to explain in a rigorous way all observed bifurcation phenomena in addition rossler s spiral type and screw type attractors have been observed from the same circuit where the nonlinear resistor has only one break point i e it is described by a 2 segment piecewise linear v i characteristic this means that extremely complicated non periodic chaotic waveforms can arise in the simplest third order uncoupled electrical circuit in which all elements except one a resistor are linear and passive and in which the constitutive relation of the nonlinear resistor is made of the simplest conceivable nonlinearity namely 2 straight line segments

a three dimensional singularly perturbed conservative system with symmetry breaking in this paper we present an analysis of a three dimensional singularly perturbed conservative system we add a constant vector in the vector field to remove one of the symmetries in the system using the geometric argument and a theorem which is derived from the implicit function theorem we prove the existence of equilibria in the system and also derive some local bifurcations of these equilibria i e saddle node bifurcations we also show that although we have two saddle nodes in the system the codimension 2 bifurcation called the cusp bifurcation is not possible more sophisticated bifurcations such as the hopf bifurcation and the bifurcation of the created periodic solution are derived by using the numerical continuation software matcont following the periodic solution we found a sequence of period doubling bifurcations which leads to the existence of infinitely many periodic solutions the coexistence of two attractors is an interesting phenomenon which is observed in this paper using asymptotic analysis we discuss the dynamics in the neighborhood of a particular line in phase space at which the competition between these attractors takes place

global dynamics for the simplified lorenz system model in this paper the global attractive sets of the simplified lorenz system are studied according to lyapunov stability theory the method for constructing the lyapunov functions that applied to the former chaotic systems does not work for the simplified lorenz system we overcome this difficulty by adding a cross term to the lyapunov functions of the simplified lorenz system

theoretical and experimental time series analysis of an inductorless chua s circuit abstract in this paper we have analyzed the time series obtained from an experimental realization of an inductorless version of chua s circuit we have also compared the experimental results with the results emerging by analysis of the time series obtained by numerical simulations of the respective model equations lyapunov exponent spectra the kaplan yorke dimension and phase space diagrams were used to show the similarities between theoretical and experimental results we were able to identify the effects of the operational amplifier simulated inductor internal resistance on the chua s circuit dynamics decreasing internal resistance for decreasing current through the circuit was responsible for the observed bifurcation route

on differences and similarities in the analysis of lorenz chen and lu systems currently it is being actively discussed the question of the equivalence of various lorenz like systems and the possibility of universal consideration of their behavior algaba et al 2013a b 2014b c chen 2013 chen and yang 2013 leonov 2013a in view of the possibility of reduction of such systems to the same form with the help of various transformations in the present paper the differences and similarities in the analysis of the lorenz the chen and the lu systems are discussed it is shown that the chen and the lu systems stimulate the development of new methods for the analysis of chaotic systems open problems are discussed

semi dualizing complexes and their auslander categories let r be a commutative noetherian ring we study r modules and complexes of such with excellent duality properties while their common properties are strong enough to admit a rich theory we count among them such potentially diverse objects as dualizing complexes for r on one side and on the other the ring itself in several ways these two examples constitute the extremes and their well understood properties serve as guidelines for our study however also the employment in recent studies of ring homomorphisms of complexes lying between these extremes is incentive

a spectral commutant lifting theorem 1991 american mathematical society first published in transactions of the american mathematical society vol 325 no 2 june 1991 by the american mathematical society

a class of initials dependent dynamical systems the dynamics of initial dependent system is investigated the potential mechanism for initial dependent property is discussed general scheme is proposed to design initial dependent dynamical system this scheme can be used for chaos control by initial setting with memristor nonlinear term is critical for emergence of chaos in autonomous dynamical systems the sampled time series in chaotic system are dependent on the initial selection of variables while the attractors are invariant for fixed parameters in this paper the dynamical behavior of a class of dynamical system is investigated at fixed parameter region it is found that the state selection is dependent on the initials and the potential mechanism is discussed it is confirmed that the system can be switched between stable state periodical state and even chaotic state by selecting appropriate initials even the parameters are fixed we think that nonlinear cross terms with higher order could account for the emergence of this behavior it indicates that initial selection and resetting can be also effective to control some chaotic systems and these chaotic systems could enhance security for possible secure communication because the chaotic attractor depends on the parameter and initials selection as well in the case of secure communication the reconstruction of phase space becomes more difficult because the attractors are changed arbitrarily thus the safety for secure keys is enhanced for chaos control when the initials are reset the controller can be removed and the system can develop to step into the desired target by itself

hidden attractor in smooth chua systems abstract the hidden oscillations a basin of attraction of which does not contain neighborhoods of equilibria have been obtained first in the 50 60s of the 20th century in automatic control systems with scalar piecewise linear nonlinearity this brings up the question about the excitation nature of hidden oscillations in the present paper it is shown that hidden oscillations can exist not only in systems with piecewise linear nonlinearity but also in smooth systems here the possibility of the existence of a hidden chaotic attractor in a modified chua s system with a smooth characteristic of nonlinear element is demonstrated

stability robustness of linear normal distributed parameter systems this paper considers the stability robustness analysis problem for linear distributed parameter systems containing known perturbation operators multiplied by uncertain parameters the nominal system operators are assumed to be normal but allowed to be unbounded the perturbation operators are confined to some relative bounded set but may be unbounded also by using the lyapunov stability criterion simple bounds on uncertain parameters are derived to ensure the stability of the perturbed systems examples are provided to illustrate the usage of the theoretical results

multistability and hidden attractors in a relay system with hysteresis abstract for nonlinear dynamic systems with switching control the concept of a hidden attractor naturally applies to a stable dynamic state that either 1 coexists with the stable switching cycle or 2 if the switching cycle is unstable has a basin of attraction that does not intersect with the neighborhood of that cycle we show how the equilibrium point of a relay system disappears in a boundary equilibrium bifurcation as the system enters the region of autonomous switching dynamics and demonstrate experimentally how a relay system can exhibit large amplitude chaotic oscillations at high values of the supply voltage by investigating a four dimensional model of the experimental relay system we finally show how a variety of hidden periodic quasiperiodic and chaotic attractors arise transform and disappear through different bifurcations

the structured singular value for linear input output operators in this paper we employ our lifting method to study the structured singular value applied to input output operators of control systems we moreover give a new criterion which guarantees that the structured singular value equals its upper bound defined by d scalings

semidualizing modules of 2 2 ladder determinantal rings abstract we continue our study of ladder determinantal rings over a field k from the perspective of semidualizing modules in particular given a ladder of variables y we show that the associated ladder determinantal ring k y i 2 y admits exactly 2 n non isomorphic semidualizing modules where n is determined from the combinatorics of the ladder y the number n is essentially the number of non gorenstein factors in a certain decomposition of y from this for each n we show explicitly how to find ladders y such that k y i 2 y admits exactly 2 n non isomorphic semidualizing modules this is in contrast to our previous work which demonstrates that large classes of ladders have exactly 2 non isomorphic semidualizing modules

on the complexity of purely complex spl mu computation and related problems in multidimensional systems in this paper the following robust control problems are shown to be np hard given a purely complex uncertainty structure spl delta determine if 1 spl mu sub spl delta m 1 for a given rational matrix m 2 spl par m spl middot spl par sub spl mu 1 for a given rational transfer matrix m s and 3 inf q spl isin h sup spl infin spl par f t q spl par sub spl mu 1 for a given linear fractional transformation f t q with rational coefficients in other words purely complex spl mu computation analysis and synthesis problems are np hard it is also shown that checking stability and computing the h sup spl infin norm of a multidimensional system are np hard problems therefore it is rather unlikely to find nonconservative polynomial time algorithms for solving the problems in complete generality

ring homomorphisms and finite gorenstein dimension the local structure of homomorphisms of commutative noetherian rings is investigated from the point of view of dualizing complexes a concept of finite gorenstein dimension which substantially weakens the notion of finite flat dimension is introduced for homomorphisms it is shown to impose structural constraints due to a remarkable equivalence of subcategories of the derived category of all modules an essential part of this study is the development of relative notions of dualizing complexes and bass numbers it is proved that the bass numbers of local homomorphisms are rigid extending a known result for local rings quasi gorenstein homomorphisms are introduced as local homomorphisms that base change a dualizing complex for the source ring into one for the target they are shown to have the stability properties of the gorenstein homomorphism that they generalize 1991 mathematics subject classification primary 13h10 13d23 14e40 secondary 13c15

the two by two spectral nevanlinna pick problem we give a criterion for the existence of an analytic 2 x 2 matrix valued function on the disc satisfying a finite set of interpolation conditions and having spectral radius bounded by 1 we also give a realization theorem for analytic functions from the disc to the symmetrised bidisc