Synchronization and Control of directed transport in chaotic ratchets via active control,” Phys

Abstract Using a technique derived from nonlinear control theory, we demonstrate that two identical inertial ratchets transporting particles in two directions can be synchronized such that both ratchets transport particles in a desired direction. This novel approach to control of directed transport is applicable when there are multiple co-existing attractors in phase space transporting particles in different directions. Numerical simulations are employed to illustrate the approach

Analysis of vibrational resonance in bi-harmonically driven plasma

The phenomenon of vibrational resonance (VR) is examined and analyzed in a bi-harmonically driven two-fluid plasma model with nonlinear dissipation. An equation for the slow oscillations of the system is analytically derived in terms of the parameters of the fast signal using the method of direct separation of motion. The presence of a high frequency externally applied electric field is found to significantly modify the system's dynamics, and consequently, induce VR. The origin of the VR in the plasma model has been identified, not only from the effective plasma potential but also from the contributions of the effective nonlinear dissipation. Beside several dynamical changes, including multiple symmetry-breaking bifurcations, attractor escapes, and reversed period-doubling bifurcations, numerical simulations also revealed the occurrence of single and double resonances induced by symmetry breaking bifurcations

Neural and behavioural changes in male periadolescent mice after prolonged nicotine-MDMA treatment

The interaction between MDMA and Nicotine affects multiple brain centres and neurotransmitter systems (serotonin, dopamine and glutamate) involved in motor coordination and cognition. In this study, we have elucidated the effect of prolonged (10 days) MDMA, Nicotine and a combined Nicotine-MDMA treatment on motor-cognitive neural functions. In addition, we have shown the correlation between the observed behavioural change and neural structural changes induced by these treatments in BALB/c mice.We observed that MDMA (2 mg/Kg body weight; subcutaneous) induced a decline in motor function, while Nicotine (2 mg/Kg body weight; subcutaneous) improved motor function in male periadolescent mice. In combined treatment, Nicotine reduced the motor function decline observed in MDMA treatment, thus no significant change in motor function for the combined treatment versus the control. Nicotine or MDMA treatment reduced memory function and altered hippocampal structure. Similarly, a combined Nicotine-MDMA treatment reduced memory function when compared with the control. Ultimately, the metabolic and structural changes in these neural systems were seen to vary for the various forms of treatment. It is noteworthy to mention that a combined treatment increased the rate of lipid peroxidation in brain tissue

Inhibition of Dopamine Receptor in Neonate Hippocampus: Immunolocalization of Post Synaptic Density Protein-95 and Dopamine Receptor in vivo

The effect of haloperidol on neonatal dopaminergic neurotransmission in the hippocampus of postnatal day 20 rats (P.20) was investigated in this study. Haloperidol blocked dopamine receptors (D2R) and inhibited D2R on the membrane of neonate neurons. For this study the 0.5 ml (20 mg/kg) of haloperidol was administered to pregnant female animals intraperitoneally a week before delivery. At day P.20, 5 control animals and 5 haloperidol treated animals were taken to the behavioral studies room for the Y maze and Novel object recognition test, which was done 7 am in the morning before mating. Electrophysiology was done with 2 control pups and 2 treated pups. Electrodes were implanted in the brain at the hippocampal region 2 mm beneath the bregma, 2 mm lateral to the midline. Anterior Posterior (AP=0), Medial Lateral (ML=2 mm). Also immunolocalization and immunofluorescence of post synaptic density protein (PSD-95), hippocampal morphology and hippocampal neurons have been done respectively. Results from this study showed a decline in memory index for the Y maze as a result of the effect of D2R blockade thereby inhibiting neurotransmission in newborns. Electrophysiology result in this study showed an increase in the root mean square (RMS) of control pups. The increase in RMS is equivalent to increase in wave burst pattern caused by neuronal excitation. Immunochemistry result showed an increase in the number of PSD-95 in the hippocampus of an increase in tyrosine hydroxylase in the hippocampus of the treated neonatal rats when compared to the control neonatal rats Immunofluorescence showed decline in the number of neurons in the haloperidol treated rats and it also caused hippocampal damage in terms of morphology. Furthermore, results from electrophysiology showed a statistical significant difference with P value 0.04229 (P<0.05) using the student t-test. These findings suggest that D2R inhibition may cause decline in memory function, impair learning in newborns and disrupt neonatal dopaminergic neurotransmissio

Vibrational resonance in an inhomogeneous medium with periodic dissipation

The role of nonlinear dissipation in vibrational resonance (VR) is investigated in an inhomogeneous system characterized by a symmetric and spatially-periodic potential, and subjected to non-uniform, state-dependent, damping and a bi-harmonic driving force. The contributions of the parameters of the high frequency signal to the system’s effective dissipation are examined theoretically in comparison to linearly-damped systems, for which the parameter of interest is the effective stiffness in the equation of slow vibration. We show that the VR effect can be enhanced by varying the nonlinear dissipation parameters; and that it can be induced by a parameter that is shared by the damping inhomogeneity and the system potential. Furthermore, we have apparently identified the origin of the nonlinear-dissipation-enhanced response: we provide evidence of its connection to an Hopf bifurcation, accompanied by monotonic attractor enlargement in the VR regime

Vibrational resonances in driven oscillators with position-dependent mass

The vibrational resonance (VR) phenomenon has received a great deal of research attention over the two decades since its introduction. The wide range of theoretical and experimental results obtained has, however, been confined to VR in systems with constant mass. We now extend the VR formalism to encompass systems with position-dependent mass (PDM).We consider a generalized classical counterpart of the quantum mechanical nonlinear oscillator with PDM. By developing a theoretical framework fordetermining the response amplitude of PDMsystems, we examine and analyse their VR phenomenona, obtain conditions for the occurrence of resonances, show that the role played by PDM can be both inductive and contributory, and suggest that PDM effects could usefully be explored to maximise the efficiency of devices being operated in VRmodes. Our analysis suggests new directions for the investigation of VR in a general class of PDM systems

Chaos Control in the Nonlinear Bloch Equations using Recursive Active Control

The problem of chaos control in the nonlinear Bloch equations is considered basedon a modified active control technique. In the proposed control scheme a recursive approach and active control mechanism are combined to design control functions that drive the nonliner Bloch equations to a steady state as well as track a desired trajectory in a systematic way. The effeciency of the proposed Recursive Active Control (RAC) is demonstrated with numerical simulations

On the numerical solution of the Gross–Pitaevskii equation

The Gross–Pitaevskii equation is solved using an approach developed for the solution of the Bogoliubov–de Gennes equations for type II superconductivity. The solution is compared with others in the literature and is shown to be easily adapted to the study of an isolated vortex recently discovered in Bose-Einstein Condensation in trapped gases.Journal of the Nigerian Association of Mathematical Physics Vol. 8 2004: pp. 9-1

The transient variation in the complexes of the low-latitude ionosphere within the equatorial ionization anomaly region of Nigeria

The quest to find an index for proper characterization and description of the dynamical response of the ionosphere to external influences and its various internal irregularities has led to the study of the day-to-day variations of the chaoticity and dynamical complexity of the ionosphere. This study was conducted using Global Positioning System (GPS) total electron content (TEC) time series, measured in the year 2011, from five GPS receiver stations in Nigeria, which lies within the equatorial ionization anomaly region. The non-linear aspects of the TEC time series were obtained by detrending the data. The detrended TEC time series were subjected to various analyses to obtain the phase space reconstruction and to compute the chaotic quantifiers, which are Lyapunov exponents LE, correlation dimension, and Tsallis entropy, for the study of dynamical complexity. Considering all the days of the year, the daily/transient variations show no definite pattern for each month, but day-to-day values of Lyapunov exponents for the entire year show a wavelike semiannual variation pattern with lower values around March, April, September and October. This can be seen from the correlation dimension with values between 2.7 and 3.2, with lower values occurring mostly during storm periods, demonstrating a phase transition from higher dimension during the quiet periods to lower dimension during storms for most of the stations. The values of Tsallis entropy show a similar variation pattern to that of the Lyapunov exponent, with both quantifiers correlating within the range of 0.79 to 0.82. These results show that both quantifiers can be further used together as indices in the study of the variations of the dynamical complexity of the ionosphere. The presence of chaos and high variations in the dynamical complexity, even in quiet periods in the ionosphere, may be due to the internal dynamics and inherent irregularities of the ionosphere which exhibit non-linear properties. However, this inherent dynamics may be complicated by external factors like geomagnetic storms. This may be the main reason for the drop in the values of the Lyapunov exponent and Tsallis entropy during storms. The dynamical behaviour of the ionosphere throughout the year, as described by these quantifiers, was discussed in this work

The comparative study of chaoticity and dynamical complexity of the low-latitude ionosphere, over Nigeria, during quiet and disturbed days

The deterministic chaotic behavior and dynamical complexity of the space plasma dynamical system over Nigeria are analyzed in this study and characterized. The study was carried out using GPS (Global Positioning System) TEC (Total Electron Content) time series, measured in the year 2011 at three GPS receiver stations within Nigeria, which lies within the equatorial ionization anomaly region. The TEC time series for the five quietest and five most disturbed days of each month of the year were selected for the study. The nonlinear aspect of the TEC time series was obtained by detrending the data. The detrended TEC time series were subjected to various analyses for phase space reconstruction and to obtain the values of chaotic quantifiers like Lyapunov exponents, correlation dimension and also Tsallis entropy for the measurement of dynamical complexity. The observations made show positive Lyapunov exponents (LE) for both quiet and disturbed days, which indicates chaoticity, and for different days the chaoticity of the ionosphere exhibits no definite pattern for either quiet or disturbed days. However, values of LE were lower for the storm period compared with its nearest relative quiet periods for all the stations. The monthly averages of LE and entropy also show no definite pattern for the month of the year. The values of the correlation dimension computed range from 2.8 to 3.5, with the lowest values recorded at the storm period of October 2011. The surrogate data test shows a significance of difference greater than 2 for all the quantifiers. The entropy values remain relatively close, with slight changes in these values during storm periods. The values of Tsallis entropy show similar variation patterns to those of Lyapunov exponents, with a lot of agreement in their comparison, with all computed values of Lyapunov exponents correlating with values of Tsallis entropy within the range of 0.79 to 0.81. These results show that both quantifiers can be used together as indices in the study of the variation of the dynamical complexity of the ionosphere. The results also show a strong play between determinism and stochasticity. The behavior of the ionosphere during these storm and quiet periods for the seasons of the year are discussed based on the results obtained from the chaotic quantifiers