Hidden attractors in dynamical systems
Dawid Dudkowski,Sajad Jafari,Tomasz Kapitaniak,Nikolay Kuznetsov,Nikolay Kuznetsov,Gennady A. Leonov,Awadhesh Prasad +6 more
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TLDR
In this paper, the authors discuss the most representative examples of hidden attractors, discuss their theoretical properties and experimental observations, and also describe numerical methods which allow identification of the hidden attractor.Citations
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Two-memristor-based Chua’s hyperchaotic circuit with plane equilibrium and its extreme multistability
TL;DR: In this article, a two-memristor-based Chua's hyper-chaotic circuit is presented, which is synthesized from an active band pass filter-based circuit through replacing a nonlinear resistor and a linear resistor with two different memristors.
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Coexistence of hidden chaotic attractors in a novel no-equilibrium system
TL;DR: In this article, the authors introduced a novel autonomous system with hidden attractor, which exhibits complex behavior such as chaos and multistability, and the offset boosting of a variable is achieved by adding a single controlled constant.
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A new finding of the existence of hidden hyperchaotic attractors with no equilibria
TL;DR: A new four-dimensional hyperchaotic system developed by extension of the generalized diffusionless Lorenz equations is presented, which does not display any equilibria, but can exhibit two-scroll hyperchaos as well as chaotic, quasiperiodic and periodic dynamics.
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Coexisting multi-stable patterns in memristor synapse-coupled Hopfield neural network with two neurons
TL;DR: In this paper, a three-order two-neuron-based autonomous memristive Hopfield neural network (HNN) is presented, which is the lowest order and has not been reported in the previous studies.
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Autonomous memristor chaotic systems of infinite chaotic attractors and circuitry realization
TL;DR: Three-dimensional, four- dimensional, and five-dimensional memristor chaotic systems are given in standard form with sine functions and tangent functions to prove the effectiveness of the method given and an analog circuit of three-dimensional memory chaotic system is designed and implemented to prove its feasibility.
References
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Canonical dynamics: Equilibrium phase-space distributions
TL;DR: The dynamical steady-state probability density is found in an extended phase space with variables x, p/sub x/, V, epsilon-dot, and zeta, where the x are reduced distances and the two variables epsilus-dot andZeta act as thermodynamic friction coefficients.
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Deterministic nonperiodic flow
TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
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A molecular dynamics method for simulations in the canonical ensemble
TL;DR: In this paper, a molecular dynamics simulation method which can generate configurations belonging to the canonical (T, V, N) ensemble or the constant temperature constant pressure ensemble was proposed, which is tested for an atomic fluid (Ar) and works well.
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Catastrophic shifts in ecosystems.
TL;DR: Recent studies show that a loss of resilience usually paves the way for a switch to an alternative state, which suggests that strategies for sustainable management of such ecosystems should focus on maintaining resilience.
Book
Chaos in dynamical systems
TL;DR: In the new edition of this classic textbook, the most important change is the addition of a completely new chapter on control and synchronization of chaos as mentioned in this paper, which will be of interest to advanced undergraduates and graduate students in science, engineering and mathematics taking courses in chaotic dynamics, as well as to researchers in the subject.