Analysis and Synchronization of a New Hyperchaotic System with Exponential Term

In this paper, a new four-dimensional hyperchaotic system with an exponential term is presented. The basic dynamical properties and chaotic behavior of the new attractor are analyzed. It can be shown that this system possesses either a line of equilibria or a single one. The existence of hyperchaos is confirmed by its Lyapunov exponents. Moreover, the synchronization problem for the hyperchaotic system is studied. Based on the Lyapunov stability theory, an adaptive control law with two inputs is proposed to achieve the global synchronization. Numerical simulations are given to validate the correctness of the proposed control law.

Synchronization of chaotic delayed systems via intermittent control and its adaptive strategy

In this paper the problem of synchronization for delayed chaotic systems is considered based on aperiodic intermittent control. First, delayed chaotic systems are proposed via aperiodic adaptive intermittent control. Next, to cut down the control gain, a new generalized intermittent control and its adaptive strategy is introduced. Then, by constructing a piecewise Lyapunov auxiliary function and making use of piecewise analysis technique, some effective and novel criteria are obtained to ensure the global synchronization of delayed chaotic systems by means of the designed control protocols. At the end, two examples with numerical simulations are provided to verify the effectiveness of the theoretical results proposed scheme.

Distinct Changes in Global Brain Synchronization in Early-Onset vs. Late-Onset Parkinson Disease

Early- and late-onset Parkinson’s disease (EOPD and LOPD, respectively) have different risk factors, clinical features, and disease course; however, the functional outcome of these differences have not been well characterized. This study investigated differences in global brain synchronization changes and their clinical significance in EOPD and LOPD patients. Patients with idiopathic PD including 25 EOPD and 24 LOPD patients, and age- and sex-matched healthy control (HC) subjects including 27 younger and 26 older controls (YCs and OCs, respectively) were enrolled. Voxel-based degree centrality (DC) was calculated as a measure of global synchronization and compared between PD patients and HC groups matched in terms of disease onset and severity. DC was decreased in bilateral Rolandic operculum and left insula and increased in the left superior frontal gyrus (SFG) and precuneus of EOPD patients compared to YCs. DC was decreased in the right putamen, mid-cingulate cortex, bilateral Rolandic operculum, and left insula and increased in the right cerebellum-crus1 of LOPD patients compared to OCs. Correlation analyses showed that DC in the right cerebellum-crus1 was inversely associated with the Hamilton Depression Scale (HDS) score in LOPD patients. Thus, EOPD and LOPD patients show distinct alterations in global synchronization relative to HCs. Furthermore, our results suggest that the left SFG and right cerebellum-crus1 play important roles in the compensation for corticostriatal–thalamocortical loop injury in EOPD and LOPD patients, whereas the cerebellum is a key hub in the neural mechanisms underlying LOPD with depression. These findings provide new insight into the clinical heterogeneity of the two PD subtypes.

Synchronization and resilience in the Kuramoto white matter network model with adaptive state-dependent delays

White matter pathways form a complex network of myelinated axons that regulate signal transmission in the nervous system and play a key role in behaviour and cognition. Recent evidence reveals that white matter networks are adaptive and that myelin remodels itself in an activity-dependent way, during both developmental stages and later on through behaviour and learning. As a result, axonal conduction delays continuously adjust in order to regulate the timing of neural signals propagating between different brain areas. This delay plasticity mechanism has yet to be integrated in computational neural models, where conduction delays are oftentimes constant or simply ignored. As a first approach to adaptive white matter remodeling, we modified the canonical Kuramoto model by enabling all connections with adaptive, phase-dependent delays. We analyzed the equilibria and stability of this system, and applied our results to two-oscillator and large-dimensional networks. Our joint mathematical and numerical analysis demonstrates that plastic delays act as a stabilizing mechanism promoting the network’s ability to maintain synchronous activity. Our work also shows that global synchronization is more resilient to perturbations and injury towards network architecture. Our results provide key insights about the analysis and potential significance of activity-dependent myelination in large-scale brain synchrony.