Entrainment by Chaos

A new phenomenon, the entrainment of limit cycles by chaos, which results from the appearance of cyclic irregular behavior, is discussed. In this study, sensitivity is considered as the main ingredient of chaos to be captured, and the period-doubling cascade is chosen for extension. Theoretical results are supported by simulations and discussions regarding Chua's oscillators, entrainment of toroidal attractors by chaos, synchronization, and controlling problems. It is demonstrated that the entrainment cannot be considered as generalized synchronization of chaotic systems.


Irreversible thermodynamics of triple junctions during the intergranular void motion under the electromigration forces
Ogurtani, TO; Oren, EE (Elsevier BV, 2005-06-01)
A rigorous reformulation of internal entropy production and the rate of entropy flow is developed for multi-component systems consisting of heterophases, interfaces and/or surfaces. The result is a well-posed moving boundary value problem describing the dynamics of curved interfaces and surfaces associated with voids and/or cracks that are intersected by grain boundaries. Extensive computer simulations are performed for void configuration evolution during intergranular motion. In particular we simulate evol...
Accuracy of the two-iteration spectral method for phase change problems
Dursunkaya, Zafer (Elsevier BV, 2006-12-01)
The accuracy of the solution of phase change problems using a spectral method is studied. Two iterations in the expansion are used to obtain the interface location of a solidification problem. in semi-infinite domain. Asymptotic expansion of the current approach is compared to the existing analytical solution of the problem, and the validity of the expansion is studied. The results indicate the accuracy of a numerical application of the current approach to finite and semi-infinite geometries. (c) 2005 Elsev...
Shunting inhibitory cellular neural networks with strongly unpredictable oscillations
Akhmet, Marat; Tleubergenova, Madina; Zhamanshin, Akylbek (Elsevier BV, 2020-10-01)
The paper considers a new type of solutions for shunting inhibitory cellular neural networks (SICNNs), strongly unpredictable oscillations. The conditions for the existence, uniqueness and stability of the solutions are determined. Numerical examples are given to show the feasibility of the obtained results.
An integrative explanation of action
Benı, Majıd Davoody (Elsevier BV, 2020-12-01)
The Predictive Processing Theory (PP) and its foundational Free Energy Principle (FEP) provide a unifying theoretical groundwork that subsumes theories of perception, cognition, and action. Recently Colin Klein (2018) contends that PP-FEP cannot explain adaptive action with the same force that they deal with perceptions. In his answer to the objection, Clark (2020) points out that FEP explains action, desire and motivation on the basis of minimisation of energy. I argue that this answer begs the question of...
Domain-Structured Chaos in a Hopfield Neural Network
Akhmet, Marat (World Scientific Pub Co Pte Lt, 2019-12-30)
In this paper, we provide a new method for constructing chaotic Hopfield neural networks. Our approach is based on structuring the domain to form a special set through the discrete evolution of the network state variables. In the chaotic regime, the formed set is invariant under the system governing the dynamics of the neural network. The approach can be viewed as an extension of the unimodality technique for one-dimensional map, thereby generating chaos from higher-dimensional systems. We show that the dis...
Citation Formats
M. Akhmet, “Entrainment by Chaos,” JOURNAL OF NONLINEAR SCIENCE, pp. 411–439, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48703.