共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper we investigate canard phenomena occurring in
oscillations of a surface oxidation reaction which can be modeled
by a three-dimensional singularly perturbed system of ordinary
differential equations with two fast variables. By using
asymptotic methods, we prove the existence of the maximal canard of
the mentioned model, and provide sufficient conditions for the
existence of stable canard cycles. 相似文献
2.
We investigate effective Newton-type methods for solving piecewise linear systems. We prove that under certain relaxed conditions the proposed Newton-type methods converge monotonically and have a finite termination property. Moreover, we give some conclusions on the existence of solution for the piecewise linear systems. 相似文献
3.
In this paper we demonstrate model order reduction of a nonlinear academic model of an inverter chain. Two reduction methods, which are suitable for nonlinear differential algebraic equation systems are combined, the trajectory piecewise linear approach and the proper orthogonal decomposition. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
4.
In this paper we provide an elementary proof of the existence of canard solutions for a class of singularly perturbed planar systems in which there occurs a transcritical bifurcation of the quasi steady states. The proof uses the one-dimensional result proved by V.F. Butuzov, N.N. Nefedov and K.R. Schneider, and an appropriate monotonicity assumption on the vector field. The result is applied to identify all possible predator–prey models with quadratic vector fields allowing for the existence of canard solutions. 相似文献
5.
Victoriano Carmona Soledad Fernández-García 《Journal of Differential Equations》2011,250(4):2244-2266
We consider the existence of periodic orbits in a class of three-dimensional piecewise linear systems. Firstly, we describe the dynamical behavior of a non-generic piecewise linear system which has two equilibria and one two-dimensional invariant manifold foliated by periodic orbits. The aim of this work is to study the periodic orbits of the continuum that persist under a piecewise linear perturbation of the system. In order to analyze this situation, we build a real function of real variable whose zeros are related to the limit cycles that remain after the perturbation. By using this function, we state some results of existence and stability of limit cycles in the perturbed system, as well as results of bifurcations of limit cycles. The techniques presented are similar to the Melnikov theory for smooth systems and the method of averaging. 相似文献
6.
Marie-Laurence Mazure 《Numerische Mathematik》2011,119(3):517-556
In the present work we determine all Chebyshevian spline spaces good for geometric design. By Chebyshevian spline space we
mean a space of splines with sections in different Extended Chebyshev spaces and with connection matrices at the knots. We
say that such a spline space is good for design when it possesses blossoms. To justify the terminology, let us recall that,
in this general framework, existence of blossoms (defined on a restricted set of tuples) makes it possible to develop all
the classical geometric design algorithms for splines. Furthermore, existence of blossoms is equivalent to existence of a
B-spline bases both in the spline space itself and in all other spline spaces derived from it by insertion of knots. We show
that Chebyshevian spline spaces good for design can be described by linear piecewise differential operators associated with
systems of piecewise weight functions, with respect to which the connection matrices are identity matrices. Many interesting
consequences can be drawn from the latter characterisation: as an example, all Chebsyhevian spline spaces good for design
can be built by means of integral recurrence relations. 相似文献
7.
Shuliang Shui Xuyang Zhang Jingjing Li 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(5):1277-1288
We use the theory of differential inclusions, Filippov transformations and some appropriate Poincaré maps to discuss the special case of two-dimensional discontinuous piecewise linear differential systems with two zones. This analysis applies to uniqueness and non-uniqueness for the initial value problem, stability of stationary points, sliding motion solutions, number of closed trajectories, existence of heteroclinic trajectories connecting two saddle points forming a heteroclinic cycle and existence of the homoclinic trajectory 相似文献
8.
The canard phenomenon occurring in planar fast-slow systems under nongeneric conditions is investigated. When the critical manifold has a non-generic fold point by using the method of asymptotic analysis combined with the recently developed blow-up technique, the existence of a canard is established and the asymptotic expansion of the parameter for which a canard exists is obtained. 相似文献
9.
B. S. Mordukhovich M. E. Sarabi 《Journal of Optimization Theory and Applications》2017,172(2):554-577
This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise linear functions recently obtained by the authors. We mainly focus here on establishing relationships between full stability of local minimizers in composite optimization and Robinson’s strong regularity of associated (linearized and nonlinearized) KKT systems. Finally, we address Lipschitzian stability of parametric variational systems with convex piecewise linear potentials. 相似文献
10.
In this work, a Hopf bifurcation at infinity in three-dimensional symmetric continuous piecewise linear systems with three zones is analyzed. By adapting the so-called closing equations method, which constitutes a suitable technique to detect limit cycles bifurcation in piecewise linear systems, we give for the first time a complete characterization of the existence and stability of the limit cycle of large amplitude that bifurcates from the point at infinity. Analytical expressions for the period and amplitude of the bifurcating limit cycles are obtained. As an application of these results, we study the appearance of a large amplitude limit cycle in a Bonhoeffer–van der Pol oscillator. 相似文献
11.
S.L.T. de Souza M. Wiercigroch I.L. Caldas J.M. Balthazar 《Chaos, solitons, and fractals》2008,38(3):864-869
In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. 相似文献
12.
In this paper we investigate the limit cycles of planar piecewise linear differential systems with two zones separated by a straight line. It is well known that when these systems are continuous they can exhibit at most one limit cycle, while when they are discontinuous the question about maximum number of limit cycles that they can exhibit is still open. For these last systems there are examples exhibiting three limit cycles.The aim of this paper is to study the number of limit cycles for a special kind of planar discontinuous piecewise linear differential systems with two zones separated by a straight line which are known as refracting systems. First we obtain the existence and uniqueness of limit cycles for refracting systems of focus-node type. Second we prove that refracting systems of focus–focus type have at most one limit cycle, thus we give a positive answer to a conjecture on the uniqueness of limit cycle stated by Freire, Ponce and Torres in Freire et al. (2013). These two results complete the proof that any refracting system has at most one limit cycle. 相似文献
13.
Guanlin Li Xiyou Chen 《Communications in Nonlinear Science & Numerical Simulation》2009,14(1):194-203
In this paper, a kind of piecewise linear chaotic system is constructed based on the Shil’nikov theorem. These systems have the same Jacobian in each equilibrium, and the piecewise linear functions in them are discontinuous, piecewise constants. The condition for the existence of the heteroclinic orbits in this kind of system is discussed. According to the separating plane and the position of the equilibriums, four different chaotic systems are given. Computer simulations confirm that the proposed method can be used to construct arbitrary chaotic attractors with multi-scrolls. 相似文献
14.
In this paper, we consider a new class of piecewise linear (PWL) systems with two virtual stable node-foci (the meaning of “virtual” is from Bernardo et al. (2008)) which exhibits periodic orbits and chaos. This fact that PWL systems have no unstable equilibria but has chaos will unavoidably make the exploration of this chaos more complicated. Particular values for bifurcation diagram are provided. Based on mathematical analysis and Poincaré map, periodic orbits of this kind of system without unstable equilibrium points are derived, the corresponding existence theorems are given, and the obtained results are applied to specific examples. 相似文献
15.
Rong Cheng 《Acta Appl Math》2010,110(1):209-214
In many fields of applications, especially in applications from mechanics, many equations of motion can be written as Hamiltonian
systems. In this paper, we study a class of asymptotically linear Hamiltonian systems. We construct a symplectic transformation
which reduces the linear systems of the Hamiltonian systems. This reduction method can be applied to study the existence of
periodic solutions for a class of asymptotically linear Hamiltonian systems under weaker conditions on the linear systems
of the Hamiltonian systems. 相似文献
16.
In this work, the issue of estimation of reachable sets in continuous bimodal piecewise affine systems is studied. A new method is proposed, in the framework of ellipsoidal bounding, using piecewise quadratic Lyapunov functions. Although bimodal piecewise affine systems can be seen as a special class of affine hybrid systems, reachability methods developed for affine hybrid systems might be inappropriately complex for bimodal dynamics. This work goes in the direction of exploiting the dynamical structure of the system to propose a simpler approach. More specifically, because of the piecewise nature of the Lyapunov function, we first derive conditions to ensure that a given quadratic function is positive on half spaces. Then, we exploit the property of bimodal piecewise quadratic functions being continuous on a given hyperplane. Finally, linear matrix characterizations of the estimate of the reachable set are derived. 相似文献
17.
Jiafu Wang Xiaoyan Chen Lihong Huang 《Journal of Mathematical Analysis and Applications》2019,469(1):405-427
The objective of this paper is to study the number and stability of limit cycles for planar piecewise linear (PWL) systems of node–saddle type with two linear regions. Firstly, we give a thorough analysis of limit cycles for Liénard PWL systems of this type, proving one is the maximum number of limit cycles and obtaining necessary and sufficient conditions for the existence and stability of a unique limit cycle. These conditions can be easily verified directly according to the parameters in the systems, and play an important role in giving birth to two limit cycles for general PWL systems. In this step, the tool of a Bendixon-like theorem is successfully employed to derive the existence of a limit cycle. Secondly, making use of the results gained in the first step, we obtain parameter regions where the general PWL systems have at least one, at least two and no limit cycles respectively. In addition for the general PWL systems, some sufficient conditions are presented for the existence and stability of a unique one and exactly two limit cycles respectively. Finally, some numerical examples are given to illustrate the results and especially to show the existence and stability of two nested limit cycles. 相似文献
18.
We consider the dynamics of planar fast-slow systems near generic transcritical type canard point. By using geometric singular perturbation theory combined with the recently developed blow-up technique, the existence of canard cycles, relaxation oscillations and solutions near the attracting branch of the critical manifold is established. The asymptotic expansion of the parameter for which canard exists is obtained by a version of the Melnikov method. 相似文献
19.
Xiaolin Huang Jun Xu Shuning Wang 《Journal of Optimization Theory and Applications》2012,155(1):145-164
Utilizing compact representations for continuous piecewise linear functions, this paper discusses some theoretical properties for nonseparable continuous piecewise linear programming. The existence of exact penalty for continuous piecewise linear programming is proved, which allows us to concentrate on unconstrained problems. For unconstrained problems, we give a sufficient and necessary local optimality condition, which is based on a model with universal representation capability and hence applicable to arbitrary continuous piecewise linear programming. From the gained optimality condition, an algorithm is proposed and evaluated by numerical experiments, where the theoretical properties are illustrated as well. 相似文献
20.
J.J. Benjamin Biemond Nathan van de Wouw Henk Nijmeijer 《Nonlinear Analysis: Hybrid Systems》2010,4(3):451-474
In this paper we present a procedure to find all limit sets near bifurcating equilibria in a class of hybrid systems described by continuous, piecewise smooth differential equations. For this purpose, the dynamics near the bifurcating equilibrium is locally approximated as a piecewise affine systems defined on a conic partition of the plane. To guarantee that all limit sets are identified, conditions for the existence or absence of limit cycles are presented. Combining these results with the study of return maps, a procedure is presented for a local bifurcation analysis of bifurcating equilibria in continuous, piecewise smooth systems. With this procedure, all limit sets that are created or destroyed by the bifurcation are identified in a computationally feasible manner. 相似文献