By introducing a feedback control to a proposed Sprott E system, an extremely complex chaotic attractor with only one stable equilibrium is derived. The system evolves into periodic and chaotic behaviors by detailed numerical as well as theoretical analysis. Analysis results show that chaos also can be generated via a period-doubling bifurcation when the system has one and only one stable equilibrium. Based on Lyapunov stability theory, the adaptive control law and the parameter update law are derived to achieve modified function projective synchronized between the extended Sprott E system and original Sprott E system. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.
Chaotic transitions likely emerge in a wide variety of cognitive phenomena and may be linked to specific changes during the development of mental disorders. They represent relatively short periods in the behavior of a system, which are extremely sensitive to very small changes. This increased sensitivity has been suggested to occur also during retrieval of stressful emotional experiences because of their fragmentary, temporally and spatially disorganized character. To test this hypothesis we recorded EEG during retrieval of fearful memories related to panic attack in 7 patients and retrieval of anxiety-related memories in 11 healthy controls. Nonlinear data analysis of EEG records showed a statistically significant increase in degree of chaotic dynamics after retrieval of stressful memories in majority of patients as well as in control subjects. This change correlated with subjective intensity of anxiety induced during the memory retrieval. The data suggest a role of nonlinear changes of neural dynamics in the processing of stressful
anxiety-related memories, which may play an important role in the pathophysiology of panic disorder.
In this paper, we present adaptive observers for synaptically coupled Hindmarsh-Rose (HR) neurons with the membrane potential measurement under the assumption that some of parameters in an individual HR neuron are known. Using the adaptive observers for a single HR neuron, we propose a two-stage merging procedure to identify the firing pattern of a model of synaptically coupled HR neurons. The procedure allows us to recover the internal states and to distinguish the firing patterns of the synaptically coupled HR neurons, with early-time dynamic behaviors.
According to recent findings activation of anterior cingulate co
rtex (ACC) is related to detecting cognitive conflict. This
conflict related activation elicits autonomic responses which can be assessed by psychophysiological measures such as
heart rate variability calculated as beat to beat R-R interv
als (RRI). Recent findings in neuroscience also suggest that
cognitive conflict is related to specific nonlinear chaotic changes of the signal generated by neural systems. The present
study used Stroop word-color test as an experimental approach to psychophysiological study of cognitive conflict in
connection with RRI measurement, psychometric measurement of limbic irritability (LSCL-33), depression (BDI-II)
and calculation of largest Lyapunov exponents in nonlinear data analysis of RRI time series. Significant correlation 0.61
between largest Lyapunov exponents and LSCL-33 found in this study indicate that a defect of neural inhibition during
conflicting Stroop task is closely related to
limbic irritability. Because limbic irritability is probably closely related to
epileptiform abnormalities in the temporolimbic structures, this result might represent useful instrument for indication
of anticonvulsant treatment in depressive patients who are resistant to antidepressant medication.