Sensitive Dependence on Parameters of Continuous-time Nonlinear Dynamical Systems
نویسندگان
چکیده
The sensitive dependence of periodicity and chaos on parameters is investigated for three-dimensional nonlinear dynamical systems. Previous works have found that noninvertible low-dimensional maps present power-law exponents relating the uncertainty between periodicity and chaos to the precision on the system parameters. Furthermore, the values obtained for these exponents have been conjectured to be universal in these maps. However, confirmation of the observed exponent values in continuous-time systems remain an open question. In this work, we show that one of these exponents can also be found in different classes of three-dimensional continuous-time dynamical systems, suggesting that the sensitive dependence on parameters of deterministic nonlinear dynamical systems is typical.
منابع مشابه
The Exact Solution of Min-Time Optimal Control Problem in Constrained LTI Systems: A State Transition Matrix Approach
In this paper, the min-time optimal control problem is mainly investigated in the linear time invariant (LTI) continuous-time control system with a constrained input. A high order dynamical LTI system is firstly considered for this purpose. Then the Pontryagin principle and some necessary optimality conditions have been simultaneously used to solve the optimal control problem. These optimality ...
متن کاملSynchronization criteria for T-S fuzzy singular complex dynamical networks with Markovian jumping parameters and mixed time-varying delays using pinning control
In this paper, we are discuss about the issue of synchronization for singular complex dynamical networks with Markovian jumping parameters and additive time-varying delays through pinning control by Takagi-Sugeno (T-S) fuzzy theory.The complex dynamical systems consist of m nodes and the systems switch from one mode to another, a Markovian chain with glorious transition probabili...
متن کاملThe Study of Nonlinear Dynamical Systems Nuclear Fission Using Hurwitz Criterion
In this paper, the nonlinear dynamic system of equations, a type of nuclear ssion reactor is solved analytically and numerically. Considering that the direct solution of three-dimensional dynamical systems analysis and more in order to determine the stability and instability, in terms of algebraicsystems is dicult. Using certain situations in mathematics called Hurwitz criterion, Necessary and ...
متن کاملTutorial and Review on the Synchronization of Chaotic Dynamical Systems
1990s researchers have realized that chaotic systems can be synchronized. The phenomenon chaotic synchronization is immediately interesting because of its high potential for applications. Our purpose in this paper is to collect results from various areas in a review article format with a tutorial emphasis. Chaotic dynamical systems having features, sensitive dependence on initial conditions and...
متن کاملStable Rough Extreme Learning Machines for the Identification of Uncertain Continuous-Time Nonlinear Systems
Rough extreme learning machines (RELMs) are rough-neural networks with one hidden layer where the parameters between the inputs and hidden neurons are arbitrarily chosen and never updated. In this paper, we propose RELMs with a stable online learning algorithm for the identification of continuous-time nonlinear systems in the presence of noises and uncertainties, and we prove the global ...
متن کامل