Fractional-order biological system: chaos, multistability and coexisting attractors

Complex bio rhythms

“…Ramakrishnan et al [ 26 ] realize the analysis and field programmable gate arrays (FPGA) implementation of a resistive-capacitive-inductive shunted Josephson junction (RCLSJJ) circuit with topologically nontrivial barrier (TNB). The fractional incommensurate order of Van der Pol equations to explain the nonlinear dynamics of a biological system is investigated in Debbouche et al [ 27 ]. Finally, the paper by Added et al [ 28 ] focuses on the regulation of the complicated and rhythmic behaviors of the bipedal compass-type robot’s passive dynamic walk.…”

A new fractional-order complex chaotic system with extreme multistability and its implementation

“…In recent years, fractional-order has become a hot research topic because of the development of mathematics and the nonlinear motion. Fractional-order calculus has long memory property and global nature, which can describe various physical models in nature more accurately [1][2][3][4]. Scholars found that the chaotic properties are more complex after the introduction of the fractional-order calculus, and it has richer dynamics and applications [5][6][7][8][9].…”

Dynamical investigation and FPGA implementation of a new Heartbeat model based on the Barrio-Varea-Aragon-Maini oscillator

“…Various physical, chemical, biological or ecological phenomena, etc can be modelled thanks to mathematics, and then be analysed in order to predict their future behaviour and anticipate, for example, the action to be taken depending on whether the occurrence of the said behaviour will prove beneficial or harmful. In the theory of dynamic systems, these behaviours include among others: The route to chaos phenomenon highlighted in a neuron model [1][2][3] the chaotic dynamics characterised by sensitivity to initial conditions and highlighted in a system of interacting nephrons [4]; the coexistence of attractors [5,6], the antimonotonicity [7,8] and the hysteresis [9][10][11], just to name a few. To predict these different phenomena in a given system, several analysis tools for dynamic systems are needed, including : Time series, which allow the trajectory of the system to be observed over time; phase portraits, which characterise the presence of an attractor; bifurcation diagrams, which indicate the values taken asymptotically by a system as a function of its control parameter; the Lyapunov exponent, which provides information on the degree of sensitivity of the system to its initial conditions; and basins of attraction, which provide information on the set of initial conditions for which the trajectories of the system converge towards one of its attractors.…”