5 results
Search Results
2. Fractional-Order Hidden Attractor Based on the Extended Liu System
- Author
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Ling Liu, Xinshan Cai, Chongxin Liu, Yaoyu Wang, Guangchao Zheng, and Yan Wang
- Subjects
Equilibrium point ,Article Subject ,Computer simulation ,General Mathematics ,General Engineering ,Chaotic ,Fixed point ,Engineering (General). Civil engineering (General) ,01 natural sciences ,010305 fluids & plasmas ,Flow (mathematics) ,Control theory ,Stability theory ,0103 physical sciences ,Attractor ,QA1-939 ,Applied mathematics ,TA1-2040 ,010301 acoustics ,Mathematics - Abstract
In this paper, a new commensurate fractional-order chaotic oscillator is presented. The mathematical model with a weak feedback term, which is named hypogenetic flow, is proposed based on the Liu system. And with changing the parameters of the system, the hidden attractor can have no equilibrium points or line equilibrium. What is more interesting is that under the occasion that no equilibrium point can be obtained, the phase trajectory can converge to a minimal field under the lead of some initial conditions, similar to the fixed point. We call it the virtual equilibrium point. On the other hand, when the value of parameters can produce an infinite number of equilibrium points, the line equilibrium points are nonhyperbolic. Moreover than that, there are coexistence attractors, which can present hyperchaos, chaos, period, and virtual equilibrium point. The dynamic characteristics of the system are analyzed, and the parameter estimation is also studied. Then, an electronic circuit implementation of the system is built, which shows the feasibility of the system. At last, for the fractional system with hidden attractors, the finite-time synchronization control of the system is carried out based on the finite-time stability theory of the fractional system. And the effectiveness of the controller is verified by numerical simulation.
- Published
- 2020
3. Global Dynamics of a Generalized SIRS Epidemic Model with Constant Immigration
- Author
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Qianqian Cui, Qinghui Du, and Li Wang
- Subjects
Invariance principle ,Article Subject ,General Mathematics ,010102 general mathematics ,General Engineering ,Engineering (General). Civil engineering (General) ,01 natural sciences ,Stability (probability) ,Quantitative Biology::Other ,Complement (complexity) ,010101 applied mathematics ,Stability theory ,QA1-939 ,Applied mathematics ,Quantitative Biology::Populations and Evolution ,0101 mathematics ,TA1-2040 ,Epidemic model ,Constant (mathematics) ,Basic reproduction number ,Mathematics ,Lyapunov direct method - Abstract
In this paper, we discuss the global dynamics of a general susceptible-infected-recovered-susceptible (SIRS) epidemic model. By using LaSalle’s invariance principle and Lyapunov direct method, the global stability of equilibria is completely established. If there is no input of infectious individuals, the dynamical behaviors completely depend on the basic reproduction number. If there exists input of infectious individuals, the unique equilibrium of model is endemic equilibrium and is globally asymptotically stable. Once one place has imported a disease case, then it may become outbreak after that. Numerical simulations are presented to expound and complement our theoretical conclusions.
- Published
- 2020
4. AsynchronousH∞Estimation for Two-Dimensional Nonhomogeneous Markovian Jump Systems with Randomly Occurring Nonlocal Sensor Nonlinearities
- Author
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Ying Zhang, Rui Zhang, and Victor Sreeram
- Subjects
Nonlinear system ,Markov chain ,Control theory ,Asynchronous communication ,Bernoulli distribution ,General Mathematics ,Stability theory ,Convex polytope ,General Engineering ,Applied mathematics ,Filter (signal processing) ,Random variable ,Mathematics - Abstract
This paper is devoted to the problem of asynchronousH∞estimation for a class of two-dimensional (2D) nonhomogeneous Markovian jump systems with nonlocal sensor nonlinearity, where the nonlocal measurement nonlinearity is governed by a stochastic variable satisfying the Bernoulli distribution. The asynchronous estimation means that the switching of candidate filters may have a lag to the switching of system modes, and the varying character of transition probabilities is considered to reside in a convex polytope. The jumping process of the error system is modeled as a two-component Markov chain with extended varying transition probabilities. A stochastic parameter-dependent approach is provided for the design ofH∞filter such that, for randomly occurring nonlocal sensor nonlinearity, the corresponding error system is mean-square asymptotically stable and has a prescribedH∞performance index. Finally, a numerical example is used to illustrate the effectiveness of the developed estimation method.
- Published
- 2015
5. (M,β)-Stability of Positive Linear Systems
- Author
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Mihaela-Hanako Matcovschi and Octavian Pastravanu
- Subjects
0209 industrial biotechnology ,Ideal (set theory) ,Article Subject ,General Mathematics ,lcsh:Mathematics ,Mathematical analysis ,Linear system ,General Engineering ,010103 numerical & computational mathematics ,02 engineering and technology ,lcsh:QA1-939 ,01 natural sciences ,Stability (probability) ,System dynamics ,020901 industrial engineering & automation ,Operator (computer programming) ,lcsh:TA1-2040 ,Stability theory ,Applied mathematics ,0101 mathematics ,lcsh:Engineering (General). Civil engineering (General) ,Scaling ,Eigenvalues and eigenvectors ,Mathematics - Abstract
The main purpose of this work is to show that the Perron-Frobenius eigenstructure of a positive linear system is involved not only in the characterization of long-term behavior (for which well-known results are available) but also in the characterization of short-term or transient behavior. We address the analysis of the short-term behavior by the help of the “(M,β)-stability” concept introduced in literature for general classes of dynamics. Our paper exploits this concept relative to Hölder vectorp-norms,1≤p≤∞, adequately weighted by scaling operators, focusing on positive linear systems. Given an asymptotically stable positive linear system, for each1≤p≤∞, we prove the existence of a scaling operator (built from the right and left Perron-Frobenius eigenvectors, with concrete expressions depending onp) that ensures the best possible values for the parametersMandβ, corresponding to an “ideal” short-term (transient) behavior. We provide results that cover both discrete- and continuous-time dynamics. Our analysis also captures the differences between the cases where the system dynamics is defined by matrices irreducible and reducible, respectively. The theoretical developments are applied to the practical study of the short-term behavior for two positive linear systems already discussed in literature by other authors.
- Published
- 2016
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