Infinities of stable periodic orbits in systems of coupled oscillators

We consider the dynamical behavior of coupled oscillators with robust heteroclinic cycles between saddles that may be periodic or chaotic. We differentiate attracting cycles into types that we call phase resetting and free running depending on whether the cycle approaches a given saddle along one or many trajectories. At loss of stability of attracting cycling, we show in a phase-resetting example the existence of an infinite family of stable periodic orbits that accumulate on the cycling, whereas for a free-running example loss of stability of the cycling gives rise to a single quasiperiodic or chaotic attractor

The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability

We study the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter $\epsilon$ uncouples the system at $\epsilon=0$. Using a normal form for $N=2$ identical systems undergoing Hopf bifurcation, we explore the dynamical properties. Matching the normal form coefficients to a coupled Wilson-Cowan oscillator network gives an understanding of different types of behaviour that arise in a model of perceptual bistability. Notably, we find bistability between in-phase and anti-phase solutions that demonstrates the feasibility for synchronisation to act as the mechanism by which periodic inputs can be segregated (rather than via strong inhibitory coupling, as in existing models). Using numerical continuation we confirm our theoretical analysis for small coupling strength and explore the bifurcation diagrams for large coupling strength, where the normal form approximation breaks down

Transverse instability for non-normal parameters

We consider the behaviour of attractors near invariant subspaces on varying a parameter that does not preserve the dynamics in the invariant subspace but is otherwise generic, in a smooth dynamical system. We refer to such a parameter as ``non-normal''. If there is chaos in the invariant subspace that is not structurally stable, this has the effect of ``blurring out'' blowout bifurcations over a range of parameter values that we show can have positive measure in parameter space. Associated with such blowout bifurcations are bifurcations to attractors displaying a new type of intermittency that is phenomenologically similar to on-off intermittency, but where the intersection of the attractor by the invariant subspace is larger than a minimal attractor. The presence of distinct repelling and attracting invariant sets leads us to refer to this as ``in-out'' intermittency. Such behaviour cannot appear in systems where the transverse dynamics is a skew product over the system on the invariant subspace. We characterise in-out intermittency in terms of its structure in phase space and in terms of invariants of the dynamics obtained from a Markov model of the attractor. This model predicts a scaling of the length of laminar phases that is similar to that for on-off intermittency but which has some differences.Comment: 15 figures, submitted to Nonlinearity, the full paper available at http://www.maths.qmw.ac.uk/~eo

Electrochemical modelling of Li-ion battery pack with constant voltage cycling

In a battery pack, cell-to-cell chemical variation, or the variation in operating conditions, can possibly lead to current imbalance which can accelerate pack ageing. In this paper, the Pseudo-TwoDimensional(P2D) porous electrode model is extended to a battery pack layout, to predict the overall behaviour and the cell-to-cell variation under constant voltage charging and discharging. The algorithm used in this model offers the flexibility in extending the layout to any number of cells in a pack, which can be of different capacities, chemical characteristics and physical dimensions. The coupled electrothermal effects such as differential cell ageing, temperature variation, porosity change and their effects on the performance of the pack, can be predicted using this modelling algorithm. The pack charging voltage is found to have an impact on the performance as well as the SEI layer growth. Numerical studies are conducted by keeping the cells at different thermal conditions and the results show the necessity to increase the heat transfer coefficient to cool the pack, compared to single cell. The results show that the thermal imbalance has more impact than the change in inter-connecting resistance on the split current distribution, which accelerates the irreversible porous filling and ageing

A mass transfer based variable porosity model with particle radius change for a Lithium-ion battery

Micro pore-clogging in the electrodes due to SEI growth and other side reactions can cause adverse effects on the performance of a Lithium-ion battery. The fundamental problem of volume fraction variation and particle radius change during the charge-discharge process in a lithium-ion battery is modelled in this paper with the help of mass transfer based formulation and demonstrated on a battery with LiCoO2 chemistry. The model can handle the volume fraction change due to intercalation reaction, solvent reduction side reaction and the electrolyte density change due to side reaction contamination in the battery. The entire calculation presented in this paper models particle radius and volume fraction together and therefore gives greater accuracy in calculating the volume-specific-area of the reacting particles which is an important parameter controlling the Butler-Volmer kinetics. The mass deposit on the electrode (or loss of lithium) gives an indication of the amount of pre-lithiation required to maintain cell performance while the amount of mass deposited on the SEI helps to decide the safe operating condition for which the clogging of pores and capacity fade will be minimal. Moreover the model presented in this paper has wide applicability in analysing the stress development inside the battery due to irreversible porous filling

Plankton lattices and the role of chaos in plankton patchiness

Spatiotemporal and interspecies irregularities in planktonic populations have been widely observed. Much research into the drivers of such plankton patches has been initiated over the past few decades but only recently have the dynamics of the interacting patches themselves been considered. We take a coupled lattice approach to model continuous-in-time plankton patch dynamics, as opposed to the more common continuum type reaction-diffusion-advection model, because it potentially offers a broader scope of application and numerical study with relative ease. We show that nonsynchronous plankton patch dynamics (the discrete analog of spatiotemporal irregularity) arise quite naturally for patches whose underlying dynamics are chaotic. However, we also observe that for parameters in a neighborhood of the chaotic regime, smooth generalized synchronization of nonidentical patches is more readily supported which reduces the incidence of distinct patchiness. We demonstrate that simply associating the coupling strength with measurements of (effective) turbulent diffusivity results in a realistic critical length of the order of 100 km, above which one would expect to observe unsynchronized behavior. It is likely that this estimate of critical length may be reduced by a more exact interpretation of coupling in turbulent flows

CRITICAL REVIEW OF DRUG INDUCED CARDIOTOXICITY W.S.R. TO GARA VISHA

Cardiotoxicity is a condition when there is damage to heart muscles by a toxin. It has many causes but drug induced cardiotoxicity is more common. Agadtantra is one of the eight clinical branches of Ayurveda. It deals with Visha, their characteristics, manifestations and treatment. Cardiovascular diseases and cancer are the most common causes of death in India. Out of which, heart failure is a major cause. Cardiotoxicity is one reason for heart failure; it may cause due to some common drug categories like anticancer agents, monoclonals, antihypertensives, antidepressants etc. No specific antidote treatment for drug induced cardiotoxicity is available till now. Currently it is managed by using general line of treatment and symptomatic treatment. Gara visha (Artificial Poison) is the type of Samyogaja visha (Unnatural poison or chemically prepared poison) which is prepared by the combination of either poisonous or non-poisonous substances. Thorough literature review has been conducted on modern aspect of drug induced cardiotoxicity and classical aspect of Gara visha. It is found that there is positive correlation between drugs induced cardiotoxicity and Gara visha. Hence, it is concluded that various treatment modalities useful in Gara visha can be effective in drug induced cardiotoxicity. Present article will be helpful for researchers to explore different dimensions of treatment of drug induced cardiotoxicity

Modified electrochemical parameter estimation of NCR18650BD battery using implicit finite volume method

The Pseudo Two Dimensional (P2D) porous electrode model is less preferred for real time calculations due to the high computational expense and complexity in obtaining the wide range of electro-chemical parameters despite of its superior accuracy. This paper presents a finite volume based method for re-parametrising the P2D model for any cell chemistry with uncertainty in determining precise electrochemical parameters. The re-parametrisation is achieved by solving a quadratic form of the Butler-Volmer equation and modifying the anode open circuit voltage based on experimental values. Thus the only experimental result, needed to re-parametrise the cell, reduces to the measurement of discharge voltage for any C-rate. The proposed method is validated against the 1C discharge data and an actual drive cycle of a NCR18650BD battery with NCA chemistry when driving in an urban environment with frequent accelerations and regenerative braking events. The error limit of the present model is compared with the electro-chemical prediction of LiyCoO2 battery and found to be superior to the accuracy of the model presented in the literature

Harmonic cross-correlation decomposition for multivariate time series

This is the final version. Available from the American Physical Society via the DOI in this recordWe introduce harmonic cross-correlation decomposition (HCD) as a tool to detect and visualize features in the frequency structure of multivariate time series. HCD decomposes multivariate time series into spatiotemporal harmonic modes with the leading modes representing dominant oscillatory patterns in the data. HCD is closely related to data-adaptive harmonic decomposition (DAHD) [Chekroun and Kondrashov, Chaos 27, 093110 (2017)] in that it performs an eigendecomposition of a grand matrix containing lagged cross-correlations. As for DAHD, each HCD mode is uniquely associated with a Fourier frequency, which allows for the definition of multidimensional power and phase spectra. Unlike in DAHD, however, HCD does not exhibit a systematic dependency on the ordering of the channels within the grand matrix. Further, HCD phase spectra can be related to the phase relations in the data in an intuitive way. We compare HCD with DAHD and multivariate singular spectrum analysis, a third related correlation-based decomposition, and we give illustrative applications to a simple traveling wave, as well as to simulations of three coupled Stuart-Landau oscillators and to human EEG recordings.Engineering and Physical Sciences Research Council (EPSRC

Resonance bifurcations from robust homoclinic cycles

We present two calculations for a class of robust homoclinic cycles with symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic stability given by Krupa and Melbourne are not optimal. Firstly, we compute optimal conditions for asymptotic stability using transition matrix techniques which make explicit use of the geometry of the group action. Secondly, through an explicit computation of the global parts of the Poincare map near the cycle we show that, generically, the resonance bifurcations from the cycles are supercritical: a unique branch of asymptotically stable period orbits emerges from the resonance bifurcation and exists for coefficient values where the cycle has lost stability. This calculation is the first to explicitly compute the criticality of a resonance bifurcation, and answers a conjecture of Field and Swift in a particular limiting case. Moreover, we are able to obtain an asymptotically-correct analytic expression for the period of the bifurcating orbit, with no adjustable parameters, which has not proved possible previously. We show that the asymptotic analysis compares very favourably with numerical results.Comment: 24 pages, 3 figures, submitted to Nonlinearit