Related papers: Creating New Chaotic Signals with Reservoir Comput…
Predicting chaotic systems is crucial for understanding complex behaviors, yet challenging due to their sensitivity to initial conditions and inherent unpredictability. Probabilistic Reservoir Computing (RC) is well-suited for long-term…
Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: if the same signal is presented many times with the network in…
The problem of separation of an observed sum of chaotic signals into the individual components in the presence of noise on the path to the observer is considered. A noise threshold is found above which high-quality separation is impossible.…
Fixed point iterations are known to generate chaos, for some values in their parameter range. It is an established fact that Turing Machines are fixed point iterations. However, as these Machines operate in integer space, the standard…
Chaotic maps are very important for establishing chaos-based image encryption systems. This paper introduces a coupling chaotic system based on a certain unit transform, which can combine any two 1D chaotic maps to generate a new one with…
A particular example of chaos can be conceived in the interaction of non-linear oscillator with a harmonic gravitational wave. When we replace the linear potential forces by the therm SIN(x), the type of solution becomes subject to external…
Restarting a stochastic search process can accelerate its completion by providing an opportunity to take a more favorable path with each reset. This strategy, known as stochastic resetting, is well studied in random processes. Here, we…
Making accurate predictions of chaotic time series is a complex challenge. Reservoir computing, a neuromorphic-inspired approach, has emerged as a powerful tool for this task. It exploits the memory and nonlinearity of dynamical systems…
A matched filter maximizes the signal-to-noise ratio of a signal. In the recent work of Corron et al. [Chaos 20, 023123 (2010)], a matched filter is derived for the chaotic waveforms produced by a piecewise-linear system. Motivated by these…
With meteoric developments in communication systems and data storage technologies, the need for secure data transmission is more crucial than ever. The level of security provided by any cryptosystem relies on the sensitivity of the private…
When chaotic signals are used in practical communication systems, it is essential to control and eventually limit the spectral bandwidth occupied by these signals. One way to achieve this goal is to insert a discrete-time filter into a…
Reservoir computing (RC) is among the most promising approaches for AI-based prediction models of complex systems. It combines superior prediction performance with very low CPU-needs for training. Recent results demonstrated that quantum…
Reservoir Computing was shown in recent years to be useful as efficient to learn networks in the field of time series tasks. Their randomized initialization, a computational benefit, results in drawbacks in theoretical analysis of large…
A network of chaotic systems can be designed in such a way that the cluster patterns formed by synchronous nodes can be controlled through the coupling parameters. We present a novel approach to exploit such a network for covert…
Some new findings for chaos-based wireless communication systems have been identified recently. First, chaos has proven to be the optimal communication waveform because chaotic signals can achieve the maximum signal to noise ratio at…
The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with…
Here we define natural chaotic systems, like the earths weather and climate system, as chaotic systems which are open to the world so have constantly changing boundary conditions, and measurements of their states are subject to errors. In…
We examine synchronization between identical chaotic systems. A rigorous criteria is presented which, if satisfied, guarantees that the coupling produces linearly stable synchronous motion. The criteria can also be used to design couplings…
Certain deterministic non-linear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows…
Chaos reveals a fundamental paradox in the scientific understanding of Complex Systems. Although chaotic models may be mathematically deterministic, they are practically non-determinable due to the finite precision, which is inherent in all…