Dynamics, Volume 3, Issue 1

The damped van der Pol oscillator is a chaotic non-linear system. Small perturbations in initial conditions may result in wildly different trajectories. Controlling, or forcing, the behavior of a van der Pol oscillator is difficult to achieve through...

This work studies a two-time-scale functional system given by two jump diffusions under the scale separation by a small parameter $\epsilon \to 0$. The coefficients of the equations that govern the dynamics of the system depend on the segment process...

The present paper is devoted to the solvability of various two-point boundary value problems for the equation $y^{\left(4\right)}=f(t,y,y^{\prime },y^{″},y^{‴}),$ where the nonlinearity f may be defined on a bounded set and is needed to be continuous on a suitabl...

The damped oscillating structures recently revealed by a three parametric formula from the proton “effective” form factor data extracted of the measured total cross section ${\sigma }_{tot}^{bare}(e^{+}{e}^{-}\to p\overline{p})$ still seem to have an un...

In the cognitive and neural sciences, Bayesianism refers to a collection of concepts and methods stemming from various implementations of Bayes’ theorem, which is a formal way to calculate the conditional probability of a hypothesis being true...

The human brain is a complex network of connected neurons whose dynamics are difficult to describe. Brain dynamics are the global manifestation of individual neuron dynamics and the synaptic coupling between neurons. Membrane potential is a function...

A conventional approach to the dark energy (DE) concept is reviewed and discussed. According to it, there is absolutely no need for a novel DE component in the universe, provided that its matter–energy content is represented by a perfect fluid...

It is known that relativistic wavefunctions formally propagate beyond the light cone when the propagator is limited to the positive energy sector. By construction, this is the case for solutions of the Salpeter (or relativistic Schrödinger) equation...

Plastic deformation of DC04 steel is regarded as a nonlinear, complex, irreversible, and self-organized process. The stress–strain time series analysis provided the possibility to identify areas of (quasi-)elastic deformation, plastic deformati...

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For Hamiltonian systems with time-dependent potential, the Hamiltonian, and thus the energy, is no longer a constant of motion. However, for such systems as the parametric oscillator, i.e., an oscillator with time-dependent frequency $\omega \left(t\right)$, stil...

We describe non-equilibrium ${\varphi }^4$ theory in a hierarchical manner to develop a method for manipulating coherent fields as a toy model of introducing control into Quantum Field Theory (QFT) of the brain, which is called Quantum Brain Dynamics (QBD)....