Synchronization–desynchronization transitions in networks of circle maps with sinusoidal coupling

Coupled phase oscillators are adopted as powerful platforms in studying synchrony behaviors emerged in various systems with rhythmic dynamics. Much attention has been focused on coupled time-continuous oscillators described by differential equations. In this paper, we study the synchronization dynamics of networks of coupled circle maps as the discrete version of the Kuramoto model. Despite of its simplicity in mathematical form, it is found that discreteness may induce many interesting synchronization behaviors. Multiple synchronization and desynchronization transitions of both phases and frequencies are found with varying the coupling among circle-map oscillators. The mechanisms of these transitions are interpreted in terms of the mean-field approach, where collective bifurcation cascades are revealed for coupled circle-map oscillators.

Phase—Locking Dynamics in Coupled Circle—Map Lattices

The phase-locking dynamics in 1D and 2D lattices of non-identical coupled circle maps is explored. Aglobal phase locking can be attained via a cascade of clustering processes with the increase of the coupling strength.Collective spatiotemporal dynamics is observed when a global phase locking is reached. Crisis-induced desynchronizationis found, and its consequent spatiotemporal chaos is studied.

Frequency and Correlation Characteristic of the Hopf Bifurcation Chemical Oscillatory Patterns

The Belousov-Zhabotinski type of chemical reactions was studied. Dynamics of the unperturbed oscillating chemical system and subject to the external perturbations is considered. The system response to the external periodic perturbation near the Hopf bifurcation point has been monitored. As a response to the external periodic perturbation of system, one obtains the synchronization oscillations, two-, three-and multiperiodic ones as well as obtain two types of chaos. The kinetic of such reactions is analyzed by time series. The Fourier transforms were used to analyze the frequency characteristics of the synchronized and chaotic states giving the different harmonic spectra. As further statistical characteristics the winding numbers and variation values of trajectories are calculated using a rotational model of processes in relation to the coherence parameter joint with perturbation period. For chaotic states the autocorrelation functions and correlation dimensions, which form an approximation of a fractal dimension D, have been calculated. Additionally, Lyapunov exponents were computed. Their positive values confirmed chaotic behavior.

An Improved Gorilla Troops Optimizer Based on Lens Opposition-Based Learning and Adaptive β-Hill Climbing for Global Optimization

Gorilla troops optimizer(GTO)is a newly developed meta-heuristic algorithm,which is inspired by the collective lifestyle and social intelligence of gorillas.Similar to othermetaheuristics,the convergence accuracy and stability of GTOwill deterioratewhen the optimization problems to be solved becomemore complex and flexible.To overcome these defects and achieve better performance,this paper proposes an improved gorilla troops optimizer(IGTO).First,Circle chaotic mapping is introduced to initialize the positions of gorillas,which facilitates the population diversity and establishes a good foundation for global search.Then,in order to avoid getting trapped in the local optimum,the lens opposition-based learning mechanism is adopted to expand the search ranges.Besides,a novel local search-based algorithm,namely adaptiveβ-hill climbing,is amalgamated with GTO to increase the final solution precision.Attributed to three improvements,the exploration and exploitation capabilities of the basic GTOare greatly enhanced.The performance of the proposed algorithm is comprehensively evaluated and analyzed on 19 classical benchmark functions.The numerical and statistical results demonstrate that IGTO can provide better solution quality,local optimumavoidance,and robustness compared with the basic GTOand five other wellknown algorithms.Moreover,the applicability of IGTOis further proved through resolving four engineering design problems and training multilayer perceptron.The experimental results suggest that IGTO exhibits remarkable competitive performance and promising prospects in real-world tasks.

On the Smoothness of Conjugacy for Circle Covering Maps

A conjugaey between C1+αΣ-hyperbolic circle covering maps is C1+αif it has a positive derivative on some point in the Σ-set.