This study focuses on the analysis of a unique composition between two well-established models, known as Logistic–Gauss map. The investigation cohesively transitions to an exploration parameter space, essential for unraveling complexity dissipative mappings and understanding intricate relationships periodic structures chaotic regions. By manipulating control parameters, our approach reveals intriguing patterns, with findings enriched by extreme orbits, trajectories that connect local maximum...

This paper presents a recursive method for identifying extreme and superstable curves in the parameter space of dissipative one-dimensional maps. The begins by constructing an Archimedean spiral with constant arc length. Subsequently, it identifies calculating observable ψ. is used to locate region where ψ changes sign. When this occurs, bisection applied determine first point on desired or curve. Once initial direction established, subsequent points using additional method, iterating...

The study of billiards investigates the trajectories particles that move freely in a region and reflect elastically at boundaries. Although there is already considerable understanding about invariant spanning curves, also known as whispering gallery orbits context billiards, their determination phase space system, addition to analysis existence still an open question. Our proposal present numerical method based on Slater’s theorem, capable determining location these curves space, well...

One of the most fundamental questions in field neuroscience is emergence synchronous behaviour brain, such as phase, anti-phase, and shift-phase synchronisation. In this work, we investigate how connectivity between brain areas can influence phase angle neuronal To do this, consider connected by means excitatory inhibitory synapses, which neuron dynamics given adaptive exponential integrate-and-fire model. Our simulations suggest that connections from one area to another play a crucial role...

In the brain, excitation-inhibition balance prevents abnormal synchronous behaviour. However, known synaptic conductance intensity can be insufficient to account for undesired synchronisation. Due this fact, we consider time delay in excitatory and inhibitory conductances study its effect on neuronal work, build a network composed of adaptive integrate-and-fire neurons coupled by means delayed conductances. We observe that conductivities alter both state collective behaviour (synchronous or...

Buzz pollination is described using a mathematical model considering billiard approach. Applications to rough morphology of typical poricidal anther tomato flower (Solanum lycopersicum) experiencing vibrations applied by bumblebee (Bombus terrestris) are made. The rectangular with pore on its tip while the borders perturbed specific oscillations according vibrational properties bumblebee. Pollen grains considered as noninteracting particles that can escape through pore. Our results not only...

This work introduces the concept of Variable Size Game Theory (VSGT), in which number players a game is strategic decision made by themselves. We start discussing main examples theory: dominance, coexistence, and coordination. show that same set pay-offs can result coordination-like or coexistence-like games depending on each player type. also solve an inverse problem to find $d$-player reproduces fixation pattern VSGT. In sequel, we consider involving prosocial antisocial players, i.e.,...

Nearly half of the bee species can perform a fascinating stereotyped behavior to collect pollen grains by vibrating flowers, known as buzz pollination. During floral visit, these bees mechanically transfer vibrations produced their thoracic indirect flight muscles flower anther, inducing movement and leading them be released through small pore or slit placed at tip anther in poricidal flowers. In such release is affected vibrational buzzing bees, primarily duration velocity amplitude....

Statistical properties for the recurrence of particles in an oval billiard with a hole boundary are discussed. The is allowed to move under two different types motion: (i) counterclockwise periodic circulation fixed step length and; (ii) random movement around boundary. After injecting ensemble through we show that surviving probability without recurring - escaping from described by exponential law and slope decay proportional relative size hole. Since phase space system exhibits islands...

This article investigates the emergence of phase synchronization in a network randomly connected neurons by chemical synapses. The study uses classic Hodgkin–Huxley model to simulate neuronal dynamics under action train Poissonian spikes. In such scenario, we observed irregular spikes for specific range conductances and also that is reached when external current strong enough induce spiking activity but without overcoming coupling current. Conversely, if assumes very high values, then an...

12. Sample Survey Methods and Theory: vol. 1, Applications; 2, Theory. By M. H. Hansen, W. N. Hurwitz G. Madow. ISBN 0 471 30966 4, 30967 2. Wiley, New York, 1993. 638 pp. £32.50.

In this paper, we consider the evolution of an ensemble noninteracting classical particles confined in a closed region. Each one these experiences several elastic collisions with rigid-smooth oval-like boundary. As known literature, numerical simulations for kind system demand too much time, mostly because time spent solving transcendental equations. To deal that, highlight alternative approach to speed up search solutions equations via tangent method, which has proved be faster way solve...

The changeover from normal to super diffusion in time-dependent billiards is explained analytically. unlimited energy growth for an ensemble of bouncing particles obtained by means a two-dimensional mapping the first and second moments speed distribution function. We prove that, low initial speeds average grows with exponent number collisions boundary, therefore exhibiting diffusion. Eventually, this regime changes faster characterized corresponding For larger energies, temporary symmetry...

The Rulkov mapping is a phenomenological model that simulates the changes in neuronal membrane potential. In this work, we introduce parametric perturbation map, can be related to an unexpected behavior, such as malfunction of due pathologies. perturbed system still keeps its main characteristics, which includes periodic behavior followed by chaotic bursts. We verify existence set regions, known shrimps, embedded attractors with perturbation. Some phase space, time evolution variables and...

Numerical experiments of the statistical evolution an ensemble noninteracting particles in a time-dependent billiard with inelastic collisions reveals existence three regimes for speed ensemble, namely, diffusion plateau, normal growth/exponential decay, and stagnation. These are linked numerically to transition from Gauss-like Boltzmann-like distributions. Furthermore, different obtained analytically through velocity-space analysis. From these calculations, asymptotic root mean square...

This article investigates the emergence of phase synchronization in a network randomly connected neurons by chemical synapses. The study uses classic Hodgkin-Huxley model to simulate neuronal dynamics under action train Poissonian spikes. In such scenario, we observed irregular spikes for specific range conductances, and also that is reached when external current strong enough induce spiking activity but without overcoming coupling current. Conversely, if assumes very high values, then an...