A diagnosis of low-order dynamics in the atmosphere of Mars

Introduction: There is considerable evidence that shows that the Martian atmosphere behaves in a more regular fashion than its terrestrial counterpart [1, 2, 3, 4]. This evidence leads to the hypothesis of theMartian climate attractor being of a relatively low dimension, which, in turn, would imply the possibility of describing the state of the atmosphere by means of a relatively few degrees of freedom. We explore this hypothesis by assuming that the atmospheric total energy (TE), i.e. the sum of kinetic energy and total potential energy (gravitational potential energy plus internal energy), is confined in a few coherent structures which dynamically interact nonlinearly with each other

Reduced-order dynamics of the Martian atmospheric dynamics

In this paper we explore the possibility of deriving low-dimensional models of the dynamics of the Martian atmosphere. The analysis consists of a Proper Orthogonal Decomposition (POD) of the atmospheric streamfunction after first decomposing the vertical structure with a set of eigenmodes. The vertical modes were obtained from the quasi-geostrophic vertical structure equation. The empirical orthogonal functions (EOFs) were optimized to represent the atmospheric total energy. The total energy was used as the criterion to retain those modes with large energy content and discard the rest. The principal components (PCs) were analysed by means of Fourier analysis, so that the dominant frequencies could be identified. It was possible to observe the strong influence of the diurnal cycle and to identify the motion and vacillation of baroclinic waves

Initial distribution spread: A density forecasting approach

Ensemble forecasting of nonlinear systems involves the use of a model to run forward a discrete ensemble (or set) of initial states. Data assimilation techniques tend to focus on estimating the true state of the system, even though model error limits the value of such efforts. This paper argues for choosing the initial ensemble in order to optimise forecasting performance rather than estimate the true state of the system. Density forecasting and choosing the initial ensemble are treated as one problem. Forecasting performance can be quantified by some scoring rule. In the case of the logarithmic scoring rule, theoretical arguments and empirical results are presented. It turns out that, if the underlying noise dominates model error, we can diagnose the noise spread

Dynamics at infinity and a Hopf bifurcation arising in a quadratic system with coexisting attractors

Dynamics at infinity and a Hopf bifurcation for a Sprott E system with a very small perturbation constant are studied in this paper. By using Poincaré compactification of polynomial vector fields in R 3 , the dynamics near infinity of the singularities is obtained. Furthermore, in accordance with the centre manifold theorem, the subcritical Hopf bifurcation is analysed and obtained. Numerical simulations demonstrate the correctness of the dynamical and bifurcation analyses. Moreover, by choosing appropriate parameters, this perturbed system can exhibit chaotic, quasiperiodic and periodic dynamics, as well as some coexisting attractors, such as a chaotic attractor coexisting with a periodic attractor for a > 0 , and a chaotic attractor coexisting with a quasiperiodic attractor for a= 0. Coexisting attractors are not associated with an unstable equilibrium and thus often go undiscovered because they may occur in a small region of parameter space, with a small basin of attraction in the space of initial conditions

Descent rate models of the synchronization of the Quasi-Biennial Oscillation by the annual cycle in tropical upwelling

The response of the Quasi-Biennial Oscillation (QBO) to an imposed mean upwelling with a periodic modulation is studied, by modelling the dynamics of the zero wind line at the equator using a class of equations known as ‘descent rate’ models. These are simple mathematical models that capture the essence of QBO synchronization by focusing on the dynamics of the height of the zero wind line. A heuristic descent rate model for the zero wind line is described, and is shown to capture many of the synchronization features seen in previous studies of the QBO. Using a simple transformation, it is then demonstrated that the standard Holton-Lindzen model of the QBO can itself be put into the form of a descent rate model if a quadratic velocity profile is assumed below the zero wind line. The resulting non-autonomous ordinary differential equation captures much of the synchronization behaviour observed in the full Holton-Lindzen partial differential equation. The new class of models provides a novel framework within which to understand synchronization of the QBO, and we demonstrate a close relationship between these models and the circle map well-known in the mathematics literature. Finally, we analyse reanalysis datasets to validate some of the predictions of our descent rate models, and find statistically significant evidence for synchronization of the QBO that is consistent with model behaviour

Imperfect chimera and synchronization in a hybrid adaptive conductance based exponential integrate and fire neuron model

In this study, the hybrid conductance-based adaptive exponential integrate and fire (CadEx) neuron model is proposed to determine the effect of magnetic flux on conductance-based neurons. To begin with, bifurcation analysis is carried out in relation to the input current, resetting parameter, and adaptation time constant in order to comprehend dynamical transitions. We exemplify that the existence of period-1, period-2, and period-4 cycles depends on the magnitude of input current via period doubling and period halving bifurcations. Furthermore, the presence of chaotic behavior is discovered by varying the adaptation time constant via the period doubling route. Following that, we examine the network behavior of CadEx neurons and discover the presence of a variety of dynamical behaviors such as desynchronization, traveling chimera, traveling wave, imperfect chimera, and synchronization. The appearance of synchronization is especially noticeable when the magnitude of the magnetic flux coefficient or the strength of coupling strength is increased. As a result, achieving synchronization in CadEx is essential for neuron activity, which can aid in the realization of such behavior during many cognitive processes

Limit cycles in planar piecewise linear systems of saddle-saddle type with a nonregular separation line

The maximum number of crossing limit cycles in planar piecewise linear systems with a nonregular separating line is considered. We give the canonical form topological transformation by considering specific assumptions in the planar piecewise linear systems of saddle-saddle type with a nonregular separation line. Based on the classification of the section maps, we analyse the expressions and analytic properties of the composite maps. In particular, some parameter conditions are found that make the systems yield at least five bounded crossing limit cycles

Dynamical behavior and network analysis of an extended Hindmarsh–Rose neuron model

In this paper, the extended Hindmarsh–Rose neuron model, which considers the slow intracellular exchange of calcium ions between its store and the cytoplasm, is studied. The dynamical behavior of this neuron model is analyzed by deriving the equilibrium points, the bifurcation diagrams, and the Lyapunov exponents, in the presence of an external forcing current. Furthermore, the dynamics of the network of the extended model is investigated. Firstly, a one-dimensional ring network is constructed, and the effects of the coupling strength and the forcing current are considered on the network behavior. The results confirm the existence of chimera state in small coupling strength values. Then, a square network of the proposed model is created by adding an external excitation to the neurons and four cases of different parameters are considered. Particularly, the effects of the stimulus parameters, the external current, and the coupling strength are studied on the emergence of spiral waves