A tympanal insect ear exploits a critical oscillator for active amplification and tuning

SummaryA dominant theme of acoustic communication is the partitioning of acoustic space into exclusive, species-specific niches to enable efficient information transfer. In insects, acoustic niche partitioning is achieved through auditory frequency filtering, brought about by the mechanical properties of their ears [1]. The tuning of the antennal ears of mosquitoes [2] and flies [3], however, arises from active amplification, a process similar to that at work in the mammalian cochlea [4]. Yet, the presence of active amplification in the other type of insect ears—tympanal ears—has remained uncertain [5]. Here we demonstrate the presence of active amplification and adaptive tuning in the tympanal ear of a phylogenetically basal insect, a tree cricket. We also show that the tree cricket exploits critical oscillator-like mechanics, enabling high auditory sensitivity and tuning to conspecific songs. These findings imply that sophisticated auditory mechanisms may have appeared even earlier in the evolution of hearing and acoustic communication than currently appreciated. Our findings also raise the possibility that frequency discrimination and directional hearing in tympanal systems may rely on physiological nonlinearities, in addition to mechanical properties, effectively lifting some of the physical constraints placed on insects by their small size [6] and prompting an extensive reexamination of invertebrate audition

Control of stochastic chaos using sliding mode method

AbstractStabilizing unstable periodic orbits of a deterministic chaotic system which is perturbed by a stochastic process is studied in this paper. The stochastic chaos is modeled by exciting a deterministic chaotic system with a white noise obtained from derivative of a Wiener process which eventually generates an Ito differential equation. It is also assumed that the chaotic system being studied has some model uncertainties which are not random. The sliding mode controller with some modifications is used for stochastic chaos suppression. It is shown that the system states converge to the desired orbit in such a way that the error covariance converges to an arbitrarily small bound around zero. As some case studies, the stabilization of 1-cycle and 2-cycle orbits of chaotic Duffing and Φ6 Van der Pol systems is investigated by applying the proposed method to their corresponding stochastically perturbed systems. Simulation results show the effectiveness of the method and the accuracy of the statements proved in the paper

Mathematical methods of factorization and a feedback approach for biological systems

The first part of the thesis is devoted to factorizations of linear and nonlinear differential equations leading to solutions of the kink type. The second part contains a study of the synchronization of the chaotic dynamics of two Hodgkin-Huxley neurons by means of the mathematical tools belonging to the geometrical control theory.Comment: Ph. D. Thesis at IPICyT, San Luis Potosi, Mexico, 102 pp, 40 figs. Supervisors: Dr. H.C. Rosu and Dr. R. Fema

Network analysis of complex biological systems : boundedness of weakly reversible chemical reaction networks and conditions for synchronisation of coupled oscillators

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Passivity-Sliding Mode Control of Uncertain Chaotic Systems with Stochastic Disturbances

This paper is concerned with the stabilization problem of uncertain chaotic systems with stochastic disturbances. A novel sliding function is designed, and then a sliding mode controller is established such that the trajectory of the system converges to the sliding surface in a finite time. Using a virtual state feedback control technique, sufficient condition for the mean square asymptotic stability and passivity of sliding mode dynamics is derived via linear matrix inequality (LMI). Finally, a simulation example is presented to show the validity and advantage of the proposed method