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Stronger Forms of Sensitivity in the Dynamical System of Abelian Semigroup Actions J. Dyn. Control Syst. (IF 1.093) Pub Date : 2021-01-10 V. Renukadevi, S. Tamilselvi
In this paper, we continue the study of abelian semigroup actions of several stronger versions of sensitivity, such as syndetically sensitive, thickly sensitive and thickly syndetically sensitive. We derive some sufficient conditions for a dynamical system to have these sensitivities. Also, we prove that the minimal and sensitive system is syndetically sensitive and non-minimal M-system is thickly
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Riemann-Hilbert Boundary Value Problem with Piecewise Constant Transition Function J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-11-09 G. Giorgadze, G. Gulagashvili
We prove that, for any Fuchsian system of differential equations on the Riemann sphere, there exists a rational matrix function whose partial indices coincide with the splitting type of the canonical vector bundle induced from the Fuchsian system. From this, we obtain solution of the Riemann-Hilbert boundary value problem for piecewise constant matrix function in terms of holomorphic sections of vector
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Bifurcations of Zeros in Translated Families of Functions and Applications J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-11-09 P. Mardešić, D. Marín, J. Villadelprat
In this paper, we study the creation of zeros in a certain type of families of functions. The families studied are given by the difference of two basic functions with a translation made in the argument of one of these functions. The problem is motivated by applications in the 16th Hilbert problem and its ramifications. Here, we apply the results obtained to the study of bifurcations of critical periods
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Integrability Conditions of a Weak Saddle in a Complex Polynomial Differential System J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-11-06 Jaume Giné, Claudia Valls
We consider a complex differential system with a weak saddle at the origin and we characterize the existence of a local analytic first integral around the weak saddle. If the system does not have a fixed degree and instead the degree is arbitrarily large, the family can have a numerable infinite number of integrability cases.
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Decay Results for a Viscoelastic Problem with Nonlinear Boundary Feedback and Logarithmic Source Term J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-11-03 Mohammad M. Al-Gharabli, Adel M. Al-Mahdi, Salim A. Messaoudi
The main goal of this work is to investigate the long-time behavior of a viscoelastic equation with a logarithmic source term and a nonlinear feedback localized on a part of the boundary. In the framework of potential well, we first show the global existence. Then, we discuss the asymptotic behavior of the problem with a very general assumption on the behavior of the relaxation function g, namely,
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Control Homotopy of Trajectories J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-11-03 Eyüp Kizil
The main purpose of this paper is to establish the machinery for doing homotopy of (regular) trajectories of control systems. In a mildly different setting than our earlier work in Colonius et al. (J Differ Equ. 2005; 216:324–53), we require this time two trajectories of a (conic) control system to be homotopic by means of their control parameters and simply call them control homotopic. More precisely
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Subspaces of Maximal Singularity for Homogeneous Control Systems J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-10-31 G. M. Sklyar, S. Yu. Ignatovich
Non-local properties of non-linear systems, linear with respect to control function, are studied. We consider a class of such systems that are homogeneous at the origin. At a point different from the origin the system may be non-homogeneous, so its homogeneous approximation is of interest. However, at such points, the system may become less singular than at the origin. We describe a set of points where
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A Spectral Representation for the Entropy of Topological Dynamical Systems J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-10-29 M. Rahimi
In this paper, we follow an approach which considers the entropy of a dynamical system as a linear operator. We assign a linear operator on Lp spaces using a kernel entropy function. The case p = 2 is of special interest, since we may relate the entropy of the system in terms of the eigenvalues of the operator. The special case p = 1 also results in a local entropy map.
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Explicit Formulae for Geodesics in Left–Invariant Sub–Finsler Problems on Heisenberg Groups via Convex Trigonometry J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-10-24 L. V. Lokutsievskiy
In the present paper, we obtain explicit formulae for geodesics in some left–invariant sub–Finsler problems on Heisenberg groups \(\mathbb {H}_{2n+1}\). Our main assumption is the following: the compact convex set of unit velocities at identity admits a generalization of spherical coordinates. This includes convex hulls and sums of coordinate 2–dimensional sets, all left–invariant sub–Riemannian structures
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Correction to: On Spectral Curves and Complexified Boundaries of the Phase-Lock Areas in a Model of Josephson Junction J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-10-23 A. A. Glutsyuk, I. V Netay
The original version of this article unfortunately contained a mistake.
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Generalized Compactness for Finite Perimeter Sets and Applications to the Isoperimetric Problem J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-10-22 Abraham Enrique Muñoz Flores, Stefano Nardulli
For a complete noncompact Riemannian manifold with bounded geometry, we prove a “generalized” compactness result for sequences of finite perimeter sets with uniformly bounded volume and perimeter in a larger space obtained by adding limit manifolds at infinity. We extend previous results contained in Nardulli (Asian J Math 18(1):1–28, 2014), in such a way that the main theorem is a generalization of
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The Bifurcations and Exact Traveling Wave Solutions for a Nonlocal Hydrodynamic-Type System J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-10-12 Jianli Liang, Yi Zhang
A hydrodynamic-type system taking into account nonlocal effects is investigated. The exact traveling wave solutions including smooth solitary waves solutions, pseudo-peakons, periodic peakons, compactons, kink, and anti-kink wave solutions and so on are derived via the method of dynamical systems and the theory of singular traveling wave systems. It is worth pointing out that the uncountably infinitely
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Casimir Functions of Free Nilpotent Lie Groups of Steps 3 and 4 J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-10-07 A. V. Podobryaev
Any free nilpotent Lie algebra is determined by its rank and step. We consider free nilpotent Lie algebras of steps 3 and 4 and corresponding connected and simply connected Lie groups. We construct Casimir functions of such groups, i.e., invariants of the coadjoint representation. For free 3-step nilpotent Lie groups, we get a full description of coadjoint orbits. It turns out that general coadjoint
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Convergence to Fixed Points in One Model of Opinion Dynamics J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-10-03 Nikolai A. Bodunov, Sergei Yu. Pilyugin
In this paper, we study the limit behavior of trajectories of a nonlinear and discontinuous model of opinion dynamics based on the notion of bounded confidence. This model was previously studied in the case where the influence function has the form i(v) = v. It was shown that, under a particular condition on parameters of the system, any its trajectory tends to a fixed point. In this paper, we prove
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Liouvillian Integrability and the Poincaré Problem for Nonlinear Oscillators with Quadratic Damping and Polynomial Forces J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-09-15 Maria V. Demina, Nikolai S. Kuznetsov
The upper bound on the degrees of irreducible Darboux polynomials associated to the ordinary differential equations \( x_{tt}+\varepsilon {x_{t}}^{2}+\eta x_{t}+f(x)=0 \) with \( f(x)\in \mathbb {C}[x]\setminus \mathbb {C} \) and ε ≠ 0 is derived. The availability of this bound provides the solution of the Poincaré problem. Results on uniqueness and existence of Darboux polynomials are presented. The
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Diffusive Epidemiological Predator–Prey Models with Ratio-Dependent Functional Responses and Nonlinear Incidence Rate J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-09-12 Kwangjoong Kim, Wonhyung Choi, Inkyung Ahn
In this paper, when the predator breeds only by the prey, the relationship among the two classes of prey (susceptible and infected prey) and the predator is represented by using an epidemic model with nonlinear incidence and the response function depending on the density of the three individuals under homogeneous Dirichlet boundary conditions describing a hostile environment at its boundary. For this
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Singularities of Singular Solutions of First-Order Differential Equations of Clairaut Type J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-08-30 Kentaro Saji, Masatomo Takahashi
A first-order differential equation of Clairaut type has a family of classical solutions, and a singular solution when the contact singular set is not empty. The projection of a singular solution of Clairaut type is an envelope of a family of fronts (Legendre immersions). In these cases, the envelopes are always fronts. We investigate singular points of envelopes for first-order ordinary differential
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Swallowtail, Whitney Umbrella and Convex Hulls J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-08-25 Vyacheslav D. Sedykh
One of the singularities of the convex hull of a generic hypersurface in \(\mathbb {R}^{4}\) leads to a generic sewing of two famous surfaces, the swallowtail and the Whitney umbrella, along their self-intersection lines. We prove that germs of all such sewings at the common endpoint of the self-intersection lines are diffeomorphic to each other with respect to diffeomorphisms of the ambient space
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Multiple Solutions for a Class of System of ( p , q )-Kirchhoff Equations in ℝ N $\mathbb {R}^{N}$ J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-08-21 Qiang Chen, Caisheng Chen, Yunfeng Wei, Yanling Shi
This paper is concerned with the (p, q)-Kirchhoff type equations, for which the existence of infinitely many high energy solutions is proved by employing the symmetric mountain pass lemma. Furthermore, an \(L^{\infty }\) estimate for the solutions is given by applying the Moser iteration technique.
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Multiplicative Control Problems for Nonlinear Reaction-Diffusion-Convection Model J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-08-17 R.V. Brizitskii, Zh.Yu. Saritskaia
Global solvability of a boundary value problem for a generalized Boussinesq model is proved in the case, when reaction coefficient depends nonlinearly on concentration of substance. Maximum principle is stated for substance’s concentration. Solvability of control problem is proved, when the role of controls is played by diffusion and mass exchange coefficients from the equations and from the boundary
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Optimal Distributed Control for a Model of Homogeneous Incompressible Two-Phase Flows J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-07-28 Fang Li, Bo You
The main objective of this paper is to study the optimal distributed control for a model of homogeneous incompressible two-phase flows. We apply the well-posedness and regularity results to establish the existence of optimal controls as well as the first-order necessary optimality conditions for an associated optimal control problem in which a distributed control is applied to the fluid.
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On Chaos Behaviour of Nonlinear Lasota Equation in Lebesgue Space J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-07-28 Antoni Leon Dawidowicz, Anna Poskrobko
We concern the asymptotic behaviour of the dynamical systems induced by nonlinear Lasota equation. We study chaoticity in the sense of Devaney and strong stability of the system. In many articles authors consider the properties of the linear version of the equation. By the construction of the operator in the separable space, we can formulate the relations between the solutions of the linear equation
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Gevrey Estimates of Formal Solutions for Certain Moment Partial Differential Equations with Variable Coefficients J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-07-21 Maria Suwińska
The goal of this paper is to investigate Gevrey properties of formal solutions of certain generalized linear partial differential equations with variable coefficients. In particular, we extend the notion of moment partial differential equations to include differential operators that are not connected with kernel functions. Using the modified version of Nagumo norms and the properties of the Newton
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Prolongational Controllability and Weak Attraction for Control Affine Systems J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-07-18 Josiney A. Souza
This paper studies the concept of prolongational controllability for control affine system with piecewise constant controls. The purpose is to show the relationship between the controllability by prolongations and the notion of weak uniform attraction, presenting criteria for controllability and controllability by prolongations. The central result assures that a control affine system is controllable
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Specification Properties on Uniform Spaces J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-07-06 Fatemah Ayatollah Zadeh Shirazi, Zahra Nili Ahmadabadi, Bahman Taherkhani, Khosro Tajbakhsh
In the following text we introduce specification property (stroboscopical property) for dynamical systems on uniform space. We focus on two classes of dynamical systems: generalized shifts and dynamical systems with Alexandroff compactification of a discrete space as phase space. We prove that for a discrete finite topological space X with at least two elements, a nonempty set Γ and a self-map φ :
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Remarks on Rational Vector Fields on ℂ ℙ 1 $\mathbb {C}\mathbb {P}^{1}$ J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-06-29 Martin Klimeš, Christiane Rousseau
In this paper, we introduce geometric tools to study the families of rational vector fields of a given degree over \(\mathbb {C}\mathbb {P}^{1}\). To a generic vector field of such a parametric family, we associate several geometric objects: a periodgon, a star domain, and a translation surface. These objects generalize objects with the same name introduced in previous works on polynomial vector fields
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N -Dimensional Zero-Hopf Bifurcation of Polynomial Differential Systems via Averaging Theory of Second Order J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-06-29 S. Kassa, J. Llibre, A. Makhlouf
Using the averaging theory of second order, we study the limit cycles which bifurcate from a zero-Hopf equilibrium point of polynomial vector fields with cubic nonlinearities in \(\mathbb {R}^{n}\). We prove that there are at least 3n− 2 limit cycles bifurcating from such zero-Hopf equilibrium points. Moreover, we provide an example in dimension 6 showing that this number of limit cycles is reached
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Approximate Controllability of Second-Grade Fluids J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-06-26 Van-Sang Ngo, Geneviève Raugel
This paper deals with the controllability of the second-grade fluids, a class of non-Newtonian of differential type, on a two-dimensional torus. Using the method of Agrachev and Sarychev (J. Math Fluid Mech., 7(1):108–52 (2005)), Agrachev and Sarychev (Commun Math Phys., 265(3):673–97 (2006)), and of Shirikyan (Commun Math Phys., 266(1):123–51 (2006)), we prove that the system of second-grade fluids
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Weak Shadowing for Actions of Some Finitely Generated Groups on Non-compact Spaces and Related Measures J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-06-13 Ali Barzanouni
In this paper, we introduce the notions of topological stability, shadowing, and weak shadowing properties for actions of some finitely generated groups on non-compact metric spaces which are dynamical properties and equivalent to the classical definitions in case of compact metric spaces. Also, we extend Walter’s stability theorem to group actions on locally compact metric spaces. We show that action
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Global Dynamics and Bifurcation of Periodic Orbits in a Modified Nosé-Hoover Oscillator J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-06-13 Jaume Llibre, Marcelo Messias, Alisson C. Reinol
We perform a global dynamical analysis of a modified Nosé-Hoover oscillator, obtained as the perturbation of an integrable differential system. Using this new approach for studying such an oscillator, in the integrable cases, we give a complete description of the solutions in the phase space, including the dynamics at infinity via the Poincaré compactification. Then using the averaging theory, we prove
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Smooth Invariant Manifolds for Differential Equations with Infinite Delay J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-06-10 Lokesh Singh, Dhirendra Bahuguna
In this article, we give the existence of a smooth stable manifold which is invariant under the semiflows of the delay differential equation \( x^{\prime }= Ax(t) + Lx_t + f(t,x_t, \lambda ) \), with the assumption that the corresponding linear differential equation admits a nonuniform exponential dichotomy and the perturbation f(t, xt, λ) is small and smooth enough. We also show that the obtained
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Affine-Periodic Solutions by Asymptotic Method J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-06-08 Fei Xu, Xue Yang
We consider the existence of affine-periodic solutions to the nonlinear ordinary differential equation: $\label {ae} x^{\prime }=f(t,x) $(0.1) in ℝn, where f is continuous and ensures the existence and uniqueness of solutions with respect to initial conditions, and there exist T > 0 and Q ∈ GL(n) such that: $\label {me} f(t+T,x)=Qf(t,Q^{-1}x) \quad \forall (t,x)\in \mathbb R\times \mathbb R^{n}. $(0
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Quenching Phenomenon for A Degenerate Parabolic Equation with a Singular Boundary Flux J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-06-02 Ying Yang
A quenching phenomenon of a degenerate parabolic equation with nonlinear source and singular boundary condition in one-dimensional space is investigated. We establish the results that quenching will occur in a finite time on the boundary x = 0 or x = 1, respectively. And the blowing up of ut at the quenching point and quenching rate estimates are discussed.
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Stabilization for Euler–Bernoulli Beam Equation with Boundary Moment Control and Disturbance via a New Disturbance Estimator J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-05-29 Hua-Cheng Zhou, Hongyinping Feng
We address the output feedback stabilization for a Euler–Bernoulli beam equation with boundary moment control and disturbance. The stabilization of this system has been studied in Guo et al. (J Dyn Control Syst. 2014;20:539–58), where the controller is based on full state feedback. In order to derive the output feedback controller, we design a new disturbance estimator to estimate the total disturbance
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Blow-Up Phenomena for a Fourth-Order Parabolic Equation with a General Nonlinearity J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-05-29 Yuzhu Han
This paper is concerned with the blow-up property of solutions to an initial boundary value problem for a fourth-order parabolic equation with a general nonlinearity. It is shown, under certain conditions on the initial data, that the solutions to this problem blow up in finite time, using differential inequalities. Moreover, upper and lower bounds for the blow-up time are derived when blow-up occurs
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Nonlocal Cahn-Hilliard-Brinkman System with Regular Potential: Regularity and Optimal Control J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-05-28 Sheetal Dharmatti, Lakshmi Naga Mahendranath Perisetti
In this paper, we study an optimal control problem for nonlocal Cahn-Hilliard-Brinkman system, which models phase separation of binary fluids in porous media. The system evolves with regular potential in a two-dimensional bounded domain. We extend the existence of weak solution results for the system to prove the existence of strong solution under extra assumptions on the forcing term and initial datum
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On the Omega-Limit Sets of Planar Nonautonomous Differential Equations with Nonpositive Lyapunov Exponents J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-05-18 Xu Zhang
The well-known Poincaré-Bendixson theorem tells us that the structure of the omega-limit sets of planar autonomous differential equations can be described by fixed points, limit cycles, or finite number of fixed points together with homoclinic and heteroclinic orbits connecting them. However, this is very different for planar nonautonomous differential equations. In this paper, we study the omega-limit
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Practical Stochastic Uniform Input-to-State Stability of Perturbed Triangular Systems J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-05-01 Ines Ellouze, Hizia Khelifa
In this paper, practical stochastic uniform input-to-state stability (PSUISS) for perturbed and perturbed triangular systems depending on parameter is investigated. We present sufficient conditions for which each of this notion is preserved under triangular interconnection. Finally, an example with simulation is provided to demonstrate the applicability of our results.
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Dynamical Decomposition of Bilinear Control Systems Subject to Symmetries J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-04-27 Domenico D’Alessandro, Jonas T. Hartwig
We describe a method to analyze and decompose the dynamics of a bilinear control system subject to symmetries. The method is based on the concept of generalized Young symmetrizers of representation theory. It naturally applies to the situation where the system evolves on a tensor product space and there exists a finite group of symmetries for the dynamics which interchanges the various factors. This
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Front-like Entire Solutions for a Lotka-Volterra Weak Competition System with Nonlocal Dispersal J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-04-19 Qian Zhang, Guo-Bao Zhang
This paper is concerned with the front-like entire solutions for a Lotka-Volterra weak competition system with nonlocal dispersal. Here, an entire solution means a classical solution defined for all space and time variables. This system has traveling wavefronts and enjoys the comparison principle. Based on these traveling wavefronts, we construct some super- and sub-solutions. Then, by using the comparison
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Expansive Actions with Specification on Uniform Spaces, Topological Entropy, and the Myhill Property J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-04-01 Tullio Ceccherini-Silberstein, Michel Coornaert
We prove that every expansive continuous action with the weak specification property of an amenable group G on a compact Hausdorff space X has the Myhill property, i.e., every pre-injective continuous self-mapping of X commuting with the action of G on X is surjective. This extends a result previously obtained by Hanfeng Li in the case when X is metrizable.
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A New Carleman Inequality for a Heat Equation in Presence of Singularities and Controllability Consequences J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-03-25 D. Sadali, M. S. Moulay
In this paper, we consider a heat equation with mixed boundary conditions in a two-dimensional domain with a reentrant corner. This allows the solution to exhibit singularities near the corner as well as at the points where the mixed boundary conditions meet. The aim of this work is to establish a Carleman inequality by constructing a convenient weight function. As a consequence, we prove some control
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Approximate Controllability of a Class of Semilinear Coupled Degenerate Systems J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-03-24 Fengdan Xu, Qian Zhou, Yuanyuan Nie
In this paper, we study the approximate controllability of a class of semilinear systems governed by coupled degenerate parabolic equations. The equations may be weakly degenerate and strongly degenerate on a portion of the lateral boundary. We prove that the control systems are approximately controllable by using the Kakutani fixed point theorem and the controls can be taken to be of quasi bang-bang
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Rates of Recurrence for Free Semigroup Actions J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-03-18 Yali Liang, Cao Zhao
We consider finitely generated free semigroup actions on (X, d) and generalize Boshernitzan’s quantitative recurrence theorem to general free semigroup actions. Let G be a finitely generated free semigroup endowed with a Bernoulli probability measure \(\mathbb P_{\underline {a}}\) and \(\mathbb S\) be the corresponding continuous semigroup continuous semigroup action. Assume that, for some α > 0, the
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Essential Boundedness and Singularity in Optimal Control J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-03-11 Javier F. Rosenblueth, Gerardo Sánchez Licea
Sufficient optimality conditions for optimal control problems involving isoperimetric and mixed inequality and equality constraints are derived. The main novelty of our approach is the fact that, for such problems, discontinuous and singular solutions can be detected. In other words, our result can deal with solutions for which the proposed optimal control is not continuous, but only essentially bounded
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Piecewise-Smooth Slow–Fast Systems J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-03-04 Paulo R. da Silva, Jaime R. de Moraes
We deal with piecewise-smooth differential systems \(\dot {z}=X(z), z=(x,y)\in \mathbb {R}\times \mathbb {R}^{n-1},\) with switching occurring in a codimension one smooth surface Σ. A regularization of X is a 1-parameter family of smooth vector fields Xδ,δ > 0, satisfying that Xδ converges pointwise to X in \(\mathbb {R}^{n}\setminus {\Sigma }\), when \(\delta \rightarrow 0\). The regularized system
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Limit Cycles Bifurcating from an Invisible Fold–Fold in Planar Piecewise Hamiltonian Systems J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-03-03 Denis de Carvalho Braga, Alexander Fernandes da Fonseca, Luiz Fernando Gonçalves, Luis Fernando Mello
The aim of this article is twofold. Firstly, we study the existence of limit cycles in a family of piecewise smooth vector fields corresponding to an unfolding of an invisible fold–fold singularity. More precisely, given a positive integer k, we prove that this family has exactly k hyperbolic crossing limit cycles in a suitable neighborhood of this singularity. Secondly, we provide a complete study
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On Spectral Curves and Complexified Boundaries of the Phase-Lock Areas in a Model of Josephson Junction J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-02-28 A. A. Glutsyuk; I. V. Netay
The paper deals with a three-parameter family of special double confluent Heun equations that was introduced and studied by V. M. Buchstaber and S. I. Tertychnyi as an equivalent presentation of a model of overdamped Josephson junction in superconductivity. The parameters are \(l,\lambda ,\mu \in \mathbb {R}\). Buchstaber and Tertychnyi described those parameter values, for which the corresponding
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A Remark on Stochastic Flows in a Hilbert Space J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-02-27 Dingxuan Tang; Lijuan Gu; Zhiming Li
This paper is an extension of known results of Pesin’s entropy formula and SRB measures for random compositions of infinite-dimensional mappings to the continuous-time setting of stochastic flows. Consider a stochastic flow ϕ on a separable infinite dimensional Hilbert space preserving a probability measure μ, which is supported on a random compact set K. We show that if ϕ is C2 (on K) and satisfies
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Darboux Integrable System with a Triple Point and Pseudo-Abelian Integrals J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-02-20 Aymen Braghtha
We study pseudo-Abelian integrals associated with polynomial perturbations of Darboux integrable system with a triple point. Under some assumptions, we prove the local boundedness of the number of their zeros. Assuming that this is the only non-genericity, we prove that the number of zeros of the corresponding pseudo-Abelian integrals is bounded uniformly for nearby Darboux integrable foliations.
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Pointwise Controllability for Degenerate Parabolic Equations by the Moment Method J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-02-04 Brahim Allal; Jawad Salhi
In this paper, we study the pointwise controllability of the one-dimensional degenerate heat equation. Necessary and sufficient conditions for approximate and null controllability are proved. Our approach is mainly based on the moment method developed by Fattorini and Russell.
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On Duality in Second-Order Discrete and Differential Inclusions with Delay J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-01-17 Elimhan N. Mahmudov
The present paper studies the duality theory for the Mayer problem with second-order evolution differential inclusions with delay and state constraints. Although all the proofs in the paper relating to dual problems are carried out in the case of delay, these results are new for problems without delay, too. To this end, first we use an auxiliary problem with second-order discrete- and discrete-approximate
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Jacobi Fields in Optimal Control: One-dimensional Variations J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-01-13 Andrei Agrachev; Ivan Beschastnyi
In this paper which is closely related to the previous paper [3] we specify general theory developed there. We study the structure of Jacobi fields in the case of an analytic system and piecewise analytic control. Moreover, we consider only 1-dimensional control variations. Jacobi fields are piecewise analytic in this case but may have jump discontinuities. We derive ODEs that these fields satisfy
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On the Invariant Manifolds of the Fixed Point of a Second-Order Nonlinear Difference Equation J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-01-10 Mehmet Turan
This paper addresses the asymptotic approximations of the stable and unstable manifolds for the saddle fixed point and the 2-periodic solutions of the difference equation xn+ 1 = α + βxn− 1 + xn− 1/xn, where α > 0, \(0\leqslant \beta <1\) and the initial conditions x− 1 and x0 are positive numbers. These manifolds determine completely global dynamics of this equation. The theoretical results are supported
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Existence for Semilinear Impulsive Differential Inclusions Without Compactness J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-01-08 Yan Luo
In this paper, we establish sufficient conditions on the existence of mild solutions for semilinear impulsive differential inclusions by using Glicksberg-Ky Fan fixed point theorem with weak topology technique. We do not require the compactness of the evolution operator generated by the linear part and of the multivalued nonlinear term. An example is also presented.
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Morse-Smale Surfaced Diffeomorphisms with Orientable Heteroclinic J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-01-07 A. Morozov; O. Pochinka
In the present paper we consider preserving orientation Morse-Smale diffeomorphisms on surfaces. Using the methods of factorization and linearizing neighbourhoods we prove that such diffeomorphisms have a finite number of orientable heteroclinic orbits.
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Boundary Control Problems for the Stationary Magnetic Hydrodynamic Equations in the Domain with Non-Ideal Boundary J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-01-07 G. V. Alekseev; R. V. Brizitskii
Boundary control problems for a stationary model of magnetohydrodynamics of a viscous incompressible fluid are considered in a domain with non-ideal boundary. The role of the control is played by a tangential component of a magnetic field specified on an entire boundary. In the case when the control function is square integrable, the solvability of the control problem is proved. Under assumption that
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Approximate Controllability of Second-order Non-autonomous System with Finite Delay J. Dyn. Control Syst. (IF 1.093) Pub Date : 2020-01-03 Ankit Kumar; Ramesh K. Vats; Avadhesh Kumar
In this article, we shall study the approximate controllability of certain non-autonomous second-order nonlinear differential problems with finite delay in the infinite dimensional space. Sufficient conditions are proposed and proved for the controllability of such systems. Further, we briefly discuss the approximate controllability of impulsive as well as integro-differential problem. We establish
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On Foliations by Curves with Singularities of Positive Dimension J. Dyn. Control Syst. (IF 1.093) Pub Date : 2019-12-11 Arturo Fernández-Pérez; Gilcione Nonato Costa
We present enumerative results for holomorphic foliations by curves on \(\mathbb {P}^{n}\), n ≥ 3, with singularities of positive dimension. Some of the results presented improve previous ones due to Corrêa et al. (Annales de l’institut Fourier, 64(4):1781–1805, 2014) and Costa (Ann Fac Sci Toulouse, Math (6), 15(2):297–321, 2006). We also present an enumerative result bounding the number of isolated
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Periodic Trajectory Tracking for Control-Affine Driftless Systems on Compact Lie Groups J. Dyn. Control Syst. (IF 1.093) Pub Date : 2019-12-06 Gabriel Araújo
We treat the periodic trajectory tracking problem: given a periodic trajectory of a control-affine, left-invariant driftless system in a compact and connected Lie group G and an initial condition in G, find another trajectory of the system satisfying the initial condition given and that asymptotically tracks the periodic trajectory. We solve this problem locally (for initial conditions in a neighborhood