Kantorovich–Rubinstein–Wasserstein distance between overlapping attractor and repeller

“…Also, we calculate the Kantorovich-Rubinstein-Wasserstein distance (KRWD) between the chaotic attractor and the chaotic repeller, which reflects the degree of similarity of the attractor and repeller as sets [43]. We calculate the KRWD using a free available program code [44].…”

Section: Methodsmentioning

confidence: 99%

The Third Type of Chaos in a System of Adaptively Coupled Phase Oscillators with Higher-Order Interactions

Emelianova,

Nekorkin

2023

Mathematics

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Adaptive network models arise when describing processes in a wide range of fields and are characterized by some specific effects. One of them is mixed dynamics, which is the third type of chaos in addition to the conservative and dissipative types. In this work, we consider a more complex type of connections between network elements—simplex, or higher-order adaptive interactions. Using numerical simulation methods, we analyze various characteristics of mixed dynamics and compare them with the case of pairwise couplings. We found that mixed dynamics in the case of simplex interactions is characterized by a very high similarity of a chaotic attractor to a chaotic repeller, as well as a stronger closeness of the sum of the Lyapunov exponents of the attractor and repeller to zero. This means that in the case of three elements, the conservative properties of the system are more pronounced than in the case of two.

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“…There are some primary tools which can be utilized to study the existence of these invariant measures such as Gibbs and SBR measures [53]- [55]. The discrete approximation of the invariant measures has been provided in several works, see for example [56]- [58] and references there in.…”

Section: Proximity Of Ghost and Non-stationary Attractorsmentioning

confidence: 99%

On Ghost Attractor in Blinking Chaotic MVD Memristor-Based Circuit and its Application

Ramaswamy¹,

El-Sayed

Elsadany

et al. 2021

IEEE Access

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This work is devoted to explore the possible existence of ghost attractors in a proposed nonautonomous blinking circuit with nonlinear memristors along with their potential application. The nonlinear dynamics of new memristor-based blinking circuit are significantly influenced by the speed of random switchings between its autonomous subcircuits. So, the effects of varying stochastic switching rate on the dynamical behaviors of blinking circuit are examined. It is demonstrated that it is possible to stimulate a non-stationary chaotic attractor for the blinking circuit which is surprisingly different from the attractors of composing subcircuits which exhibit simple periodic dynamics. A sufficiently small time period for random switchings in addition to precise tuning of circuit parameters are the major requirements for establishing these ghost attractors. The fascinating features of the induced ghost attractors render them appropriate noise-like source for secure communications applications. So, we proposed a new pseudochaos encryption algorithm that exploits the memristor-based blinking circuit in a more suitable digital platform. The proposed scheme overcomes the usual degradation in performance of digital chaos due to finite precision representation of floating numbers.INDEX TERMS Memristors; pseudo-chaos encryption; ghost attractors; blinking circuit.

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Kantorovich–Rubinstein–Wasserstein distance between overlapping attractor and repeller

Cited by 20 publications

References 36 publications

Wild pseudohyperbolic attractor in a four-dimensional Lorenz system

Wild pseudohyperbolic attractor in a four-dimensional Lorenz system

The Third Type of Chaos in a System of Adaptively Coupled Phase Oscillators with Higher-Order Interactions

On Ghost Attractor in Blinking Chaotic MVD Memristor-Based Circuit and its Application

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