Extreme events in the forced Liénard system

The highest and lowest values of a function, relative to a reference axis, are known as extreme values. These include absolute maximum and absolute minimum values, which represent the highest and lowest points the function reaches across its entire domain. Within a restricted portion of the function, the highest and lowest values are referred to as local maximum and local minimum values, respectively.Periodic functions, such as sine and cosine, show extreme values at infinitely many points due...

Atoms and molecules interact through bonds (or forces): intramolecular and intermolecular. The forces are electrostatic as they arise from interactions (attractive or repulsive) between charged species (permanent, partial, or temporary charges) and exist with varying strengths between ions, polar, nonpolar, and neutral molecules. The different types of intermolecular forces are ion–dipole, dipole–dipole, hydrogen bonds, and dispersion; among these, dipole–dipole, hydrogen...

Synaptic integration mainly includes the summation of graded potentials. Graded potentials, regardless of their type, cause subtle alterations in membrane voltage, resulting in either depolarization or hyperpolarization. These incremental changes, when combined or summed, can propel the neuron toward its threshold. Consider, for example, a membrane experiencing a +15 mV shift, causing it to depolarize from -70 mV to -55 mV. In this scenario, graded potentials govern the membrane's ability to...

Electricity is generated by either electrons or ions flowing through a solution or a conducting medium. This flow of electrons or specifically electrical charge is defined as an electric current. When electrons move through a wire, they generate an electric current. It can be recalled  that in a redox reaction, electrons are lost and gained. In the spontaneous redox reaction of zinc  with copper, when zinc is immersed in a copper ion solution, a transfer of electrons from one substance to...

Intermolecular forces (IMF) are electrostatic attractions arising from charge-charge interactions between molecules. The strength of the intermolecular force is influenced by the distance of separation between molecules. The forces significantly affect the interactions in solids and liquids, where the molecules are close together. In gases, IMFs become important only under high-pressure conditions (due to the proximity of gas molecules). Intermolecular forces dictate the physical properties of...

No object with a finite mass can travel faster than the speed of light in a vacuum. This fact has an interesting consequence in the domain of extremely high gravitational fields.
The minimum speed required to launch a projectile from the surface of an object to which it is gravitationally bound so that it eventually escapes the object’s gravitational field is called the escape velocity. The escape velocity is independent of the mass of the object. Merging the idea of escape...