In this work, a chaotification technique is proposed for increasing the complexity of chaotic maps. The technique consists of adding the remainder of multiple scalings of the map’s value for the next iteration, so that the most- and least-significant digits are combined. By appropriate parameter tuning, the resulting map can achieve a higher Lyapunov exponent value, a result that was first proven theoretically and then showcased through numerical simulations for a collection of chaotic maps. As a proposed application of the transformed maps, the encryption of B-spline curves and patches was considered. The symmetric encryption consisted of two steps: a shuffling of the control point coordinates and an additive modulation. A transformed chaotic map was utilised to perform both steps. The resulting ciphertext curves and patches were visually unrecognisable compared to the plaintext ones and performed well on several statistical tests. The proposed work gives an insight into the potential of the remainder operator for chaotification, as well as the chaos-based encryption of curves and computer graphics.

In this work, the polarity balance of a novel two-dimensional hyperchaotic map is considered, and thus the corresponding manifold of conditional symmetry is coined. The unique map has a simple structure but provides direct 2-D offset boosting, which brings the possibility for the construction of conditional symmetry by introducing an absolute value function. The corresponding evolution of the discrete sequences from the system is verified by the circuit implementation based on the microcontroller of CH32V307. The pseudorandom data from the map increases its adaptability for applications in information security. The hyperchaotic sequence-injected Ant Colony Optimization (ACO), Grey Wolf Optimizer (GWO), and Sparrow Search Algorithm (SSA) show their improved performance in the optimization algorithm. Robot path planning experiments confirm that all three algorithms exhibit superior convergence performance, global search capability, and path smoothness compared with the original algorithms.

In this work, we use an Echo State Network (ESN) model, which is essentially a recurrent neural network (RNN) operating according to the reservoir computing (RC) paradigm, to classify individual ECG heartbeats using the MIT-BIH arrhythmia database. The aim is to evaluate the performance of ESN in a challenging task that involves classification of complex, unprocessed one-dimensional signals, distributed into five classes. Moreover, we investigate the performance of the ESN in the presence of (i) noise in the dynamics of the internal variables of the hidden (reservoir) layer and (ii) random variability in the activation functions of the hidden layer cells (neurons). The overall accuracy of the best-performing ESN, without noise and variability, exceeded 96% with per-class accuracies ranging from 90.2% to 99.1%, which is higher than previous studies using CNNs and more complex machine learning approaches. The top-performing ESN required only 40 min of training on a CPU (Intel i5-1235U@1.3 GHz) HP laptop. Notably, an alternative ESN configuration that matched the accuracy of a prior CNN-based study (93.4%) required only 6 min of training, whereas a CNN would typically require an estimated training time of 2–3 days. Surprisingly, ESN performance proved to be very robust when Gaussian noise was added to the dynamics of the reservoir hidden variables, even for high noise amplitudes. Moreover, the success rates remained essentially the same when random variability was imposed in the activation functions of the hidden layer cells. The stability of ESN performance under noisy conditions and random variability in the hidden layer (reservoir) cells demonstrates the potential of analog hardware implementations of ESNs to be robust in time-series classification tasks.

Dynamical Simulation Models of the Open Source Development Process: 10.4018/978-1-59140-369-2.ch008: This chapter will discuss attempts to produce formal mathematical models for dynamical simulation of the development process of Free/Open Source Software