We study global dynamics of an SIR model with vaccination, where we assume that individuals respond differently to dynamics of the epidemic. Their heterogeneous response is modeled by the Preisach hysteresis operator. We present a condition for the global stability of the infection-free equilibrium state. If this condition does not hold true, the model has a connected set of endemic equilibrium states characterized by different proportion of infected and immune individuals. In this case, we show that every trajectory converges either to an endemic equilibrium or to a periodic orbit. Under additional natural assumptions, the periodic attractor is excluded, and we guarantee the convergence of each trajectory to an endemic equilibrium state. The global stability analysis uses a family of Lyapunov functions corresponding to the family of branches of the hysteresis operator.
- MeSH
- Models, Biological MeSH
- Epidemics * MeSH
- Communicable Diseases * epidemiology MeSH
- Humans MeSH
- Vaccination MeSH
- Check Tag
- Humans MeSH
- Publication type
- Journal Article MeSH
- Research Support, Non-U.S. Gov't MeSH
One of the key results of the food web theory states that the interior equilibrium of a tri-trophic food chain described by the Lotka-Volterra type dynamics is globally asymptotically stable whenever it exists. This article extends this result to food webs consisting of several food chains sharing a common resource. A Lyapunov function for such food webs is constructed and asymptotic stability of the interior equilibrium is proved. Numerical simulations show that as the number of food chains increases, the real part of the leading eigenvalue, while still negative, approaches zero. Thus the resilience of such food webs decreases with the number of food chains in the web.
Competition in di- and tri-trophic food web modules with many competing species is studied. The food web modules considered are apparent competition between n species sharing a single predator and a diamond-like food web with a single resource, a single top predator and many competing middle species. The predators have either fixed preferences for their prey, or they switch between available prey in a way that maximizes their fitness. Dependence of these food web dynamics on environmental carrying capacity and food web connectance is studied. The results predict that optimal flexible foraging strongly weakens apparent competition and promotes species coexistence. Food web robustness (defined here as the proportion of surviving species) does not decrease with increased connectance in these food-webs. Moreover, it is shown that flexible prey switching leads to the same population equilibria as in corresponding food webs with highly specialized predators. The results show that flexible foraging behavior by predators can have very strong impact on species richness, as well as the response of communities to changes in resource enrichment and food-web connectance when compared to the same food-web topology with inflexible top predators. Several results on global stability using Lyapunov functions are provided.
There is evidence that schizophrenic associations display "chaotic", random-like behavior and decreased predictability. The evidence suggests a hypothesis that the "chaotic" mental disorganization could be explained within the concept of nonlinear dynamics and complexity in the brain that may cause chaotic neural organization. Testing of the hypothesis in the present study was performed using nonlinear analysis of bilateral electrodermal activity (EDA) during resting state and an association test in 56 schizophrenic patients and 44 healthy participants. EDA is a suitable measure of brain and autonomic activity reflecting neurobiological changes in schizophrenia that may indicate changes in nonlinear neural dynamics related to associative process. The results show that quantitative indices of chaotic dynamics (the largest Lyapunov exponents) calculated from EDA signals recorded during rest and the association test are significantly higher in schizophrenia patients than in the control group and increase during the test in comparison to the resting state. The difference was confirmed by statistical methods and using surrogate data testing that rejected an explanation within the linear statistical framework. The results provide supportive evidence that pseudo-randomness of schizophrenic associations and less predictability could be linked to increased complexity of nonlinear neural dynamics, although certain limitations in data interpretation must be taken into account.
- MeSH
- Association MeSH
- Time Factors MeSH
- Adult MeSH
- Galvanic Skin Response physiology MeSH
- Humans MeSH
- Metaphor MeSH
- Young Adult MeSH
- Nonlinear Dynamics MeSH
- Statistics, Nonparametric MeSH
- Neuropsychological Tests MeSH
- Reality Testing MeSH
- Models, Psychological MeSH
- Schizophrenic Psychology MeSH
- Schizophrenia physiopathology MeSH
- Check Tag
- Adult MeSH
- Humans MeSH
- Young Adult MeSH
- Male MeSH
- Female MeSH
- Publication type
- Research Support, Non-U.S. Gov't MeSH
Recent findings in cognitive neuroscience indicate that activation of anterior cingulate cortex (ACC) is related to detecting cognitive conflict. Conflict related ACC activation elicits responses in central autonomic network which can be assessed by psychophysiological measures such as heart rate variability (i.e. beat to beat R-R intervals--RRI). Recent findings in neuroscience also suggest that cognitive conflict is related to specific nonlinear chaotic changes of the signal generated by the neural systems. The present study used Stroop word-colour test as an experimental approach to the study of cognitive conflict in connection with RRI measurement, psychometric measurement of dissociation (DES) and calculation of largest Lyapunov exponents in nonlinear data analysis of RRI time series in 40 patients with unipolar depression and 35 healthy controls. Significant correlation 0.58 (p<0.01) between largest Lyapunov exponents and DES found in depressive patients indicate that cognitive conflict related neural interference during conflicting Stroop task is closely related to dissociative processes. These results present first supportive evidence that degree of chaos could be related to dissociation.
- MeSH
- Depressive Disorder complications physiopathology psychology MeSH
- Dissociative Disorders complications physiopathology MeSH
- Adult MeSH
- Financing, Organized MeSH
- Cognition MeSH
- Conflict, Psychological MeSH
- Middle Aged MeSH
- Humans MeSH
- Nonlinear Dynamics MeSH
- Heart Rate physiology MeSH
- Check Tag
- Adult MeSH
- Middle Aged MeSH
- Humans MeSH
- Male MeSH
- Female MeSH
OBJECTIVE: According to recent findings detecting a cognitive conflict is related to activation of anterior cingulate cortex (ACC) and central autonomic network. Several recent findings also suggest the hypothesis that the cognitive conflict is related to specific nonlinear chaotic changes of the neural signal. 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 intervals (RRI). METHOD: The present study used Stroop word-colour test as an experimental approach to psychophysiological study of cognitive conflict in connection with RRI measurement, assessment of serum cortisol and calculation of largest Lyapunov exponents in nonlinear data analysis of RRI time series in 30 patients with unipolar depression. RESULTS: Significant correlation -0.45 (p<0.01) between largest Lyapunov exponents during conflicting Stroop task and serum cortisol levels has been found. CONCLUSIONS: The study indicates that a defect of neural inhibition during conflicting Stroop task is closely related to decreased serum cortisol levels which probably reflect defense psychological mechanisms.
- MeSH
- Gyrus Cinguli physiopathology MeSH
- Depressive Disorder blood physiopathology MeSH
- Adult MeSH
- Electrocardiography MeSH
- Financing, Organized MeSH
- Hydrocortisone blood MeSH
- Cognition physiology MeSH
- Middle Aged MeSH
- Humans MeSH
- Neuropsychological Tests MeSH
- Task Performance and Analysis MeSH
- Heart Rate MeSH
- Check Tag
- Adult MeSH
- Middle Aged MeSH
- Humans MeSH
- Male MeSH
- Female MeSH
- Publication type
- Clinical Trial MeSH
According to recent findings activation of anterior cingulate cortex (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 intervals (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.
- MeSH
- Gyrus Cinguli physiopathology MeSH
- Depressive Disorder diagnosis MeSH
- Adult MeSH
- Cognition physiology MeSH
- Conflict, Psychological * MeSH
- Humans MeSH
- Neuropsychological Tests MeSH
- Psychomotor Performance MeSH
- Check Tag
- Adult MeSH
- Humans MeSH
- Male MeSH
- Female MeSH
- Publication type
- Journal Article MeSH
- Research Support, Non-U.S. Gov't MeSH
