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This paper will show that a “simple” differential equation modeling a garden-variety damped forced pendulum can exhibit extraordinarily complicated and unstable behavior.While instability and control ...
The Hodgkin–Huxley model was developed to characterize the action potential of a squid axon. It has served as an archetype for compartmental models of the electrophysiology of biological membranes. ...
In keeping with the spirit of the Colston conference on Nonlinear Dynam- ics and Chaos, this chapter emphasizes ideas more than details, describing my vision of how the bifurcation theory of multipl...
Genetic oscillatory networks can be mathematically modeled with delay differential equations (DDEs). Interpreting genetic networks with DDEs gives a more intuitive understanding from a biological stan...
In this paper, we study Gaussian multiplicative chaos in the critical case. We show that the so-called derivative martingale, introduced in the context of branching Brownian motions and branching rand...
Abstract: We show that, for sequences of vectors of multiple Wigner integrals with respect to a free Brownian motion, componentwise convergence to semicircular is equivalent to joint convergence. This...
Abstract: The paper builds upon a recent approach to find the approximate bounds of a real function using Polynomial Chaos expansions. Given a function of random variables with compact support probabi...
We analyze, from a theoretical viewpoint, the bidirectional interdisciplinary relation between mathematics and psychology, focused on the mathematical theory of deterministic dynamical systems, and in...
A chaotic system under periodic forcing can develop a periodically visited strange attractor. We discuss simple models in which the phenomenon, quite easy to see in numerical simulations, can be com...
Many growing phenomena in both nature and society can be predicted with sigmoid function. The growth curve of the level of urbanization is a typical S-shaped one, and can be described by using logisti...
In recent years there has been a considerable increase in the publishing of textbooks and mono- graphs covering what was formerly known as random or irregular deterministic motion, now named by the ...
In this paper, we discuss the relationship between Li-Yorke chaos and distributional chaos in a sequence.
Collective stable chaos consists of the persistence of disordered patterns in dynamical spatiotem-poral systems possessing a negative maximum Lyapunov exponent. We analyze the role of the topology of ...
In this paper, we define a new criterion to identify a dynamical system and apply control laws in a simpler manner. We study chaos synchronization by using linear feedback control laws for generalized...
Analytically control term has been determined to control chaos in the problem of a satellite. Computational studies reveal the suppression of chaos which is in good agreement with the analytical inves...

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