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Although many mathematical models have been presented for glucose and insulin interaction, none of these models can describe diabetes disease completely. In this work, the dynamical behavior of a regulatory system of glucose-insulin incorporating time delay is studied and a new property of the presented model is revealed. This property can describe the diabetes disease better and therefore may help us in deeper understanding of diabetes, interactions between glucose and insulin, and possible cures for this widespread disease.

Parkinson’s and Huntington’s diseases are two of the most common neurodegenerative disorders. Tremor, muscle stiffness, and slowness of movement are symptoms of Parkinson’s disease. The symptoms of Huntington’s disease are severe reduction in muscle control, emotional disturbance, and pathological disorders in brain cells. These diseases are caused by destruction of the cells that secrete a substance called dopamine. In this paper, a new discrete chaotic system is introduced, which can mimic the brain’s behavior for neurodegenerative diseases such as Parkinson, Huntington, and Hypokinesia. This system is described based on the similarity between the brain’s behavior in normal and abnormal conditions and the chaotic systems. Bifurcation analysis is carried out with respect to different parameters, providing full spectrum of the behavior for different parameter values. Our results can be used to mathematically study the mechanisms behind these diseases.

In this paper, a new two-dimensional nonlinear oscillator with an unusual sequence of rational and irrational parameters is introduced. This oscillator has endless coexisting limit cycles, which make it a megastable dynamical system. By periodically forcing this system, a new system is designed which is capable of exhibiting an infinite number of coexisting asymmetric torus and strange attractors. This system is implemented by an analog circuit, and its Hamiltonian energy is calculated.

ProblemVia a network analysis approach, following 2 weeks of the medication Ritalin, the present study investigated the quality of symptom interactions and the pattern of behavior changes to identify locations of functional weaknesses in the network interactions of symptomology.MethodsRitalin® prescribed for 112 children (aged 4–14) with attention deficit hyperactivity disorder (ADHD) as diagnosed by five child and adolescent psychiatrists. Their parents completed Swanson, Nolan, and Pelham‐IV questionnaire (SNAP‐IV) before and after Ritalin® onset as the pre and post‐test, respectively. Then, the network analysis approach was used to discover the pattern of changes in symptom interactions.FindingsThe results indicated that in 2 weeks following its initiation, Ritalin significantly reduced restlessness and interactions between symptoms of impulsivity. “Inability to follow instructions” and “difficulty waiting their turn” symptoms were the most central symptoms of strength. Three symptoms, “Often has difficulty waiting their turn,” “runs and climbs in situations where it is inappropriate” and “does not follow through on instructions,” had the most expected influence. In the 14‐day period of investigation, Ritalin® was effective in breaking some interactions and components of ADHD, but no significant mitigation of other components of the detected symptomatology network.ConclusionFollow‐up investigations using network analysis can clarify the dynamics of the network changes after initiation of medications.