Dynamics of neural fields with exponential temporal kernel
Theory Biosci. 2024 Mar 9. doi: 10.1007/s12064-024-00414-7. Online ahead of print.ABSTRACTWe consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of...
Source: Theory in Biosciences - March 9, 2024 Category: Biology Authors: Elham Shamsara Marius E Yamakou Fatihcan M Atay J ürgen Jost Source Type: research
Dynamics of neural fields with exponential temporal kernel
Theory Biosci. 2024 Mar 9. doi: 10.1007/s12064-024-00414-7. Online ahead of print.ABSTRACTWe consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of...
Source: Theory in Biosciences - March 9, 2024 Category: Biology Authors: Elham Shamsara Marius E Yamakou Fatihcan M Atay J ürgen Jost Source Type: research
Dynamics of neural fields with exponential temporal kernel
Theory Biosci. 2024 Mar 9. doi: 10.1007/s12064-024-00414-7. Online ahead of print.ABSTRACTWe consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of...
Source: Theory in Biosciences - March 9, 2024 Category: Biology Authors: Elham Shamsara Marius E Yamakou Fatihcan M Atay J ürgen Jost Source Type: research
Dynamics of neural fields with exponential temporal kernel
Theory Biosci. 2024 Mar 9. doi: 10.1007/s12064-024-00414-7. Online ahead of print.ABSTRACTWe consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of...
Source: Theory in Biosciences - March 9, 2024 Category: Biology Authors: Elham Shamsara Marius E Yamakou Fatihcan M Atay J ürgen Jost Source Type: research
Dynamics of neural fields with exponential temporal kernel
Theory Biosci. 2024 Mar 9. doi: 10.1007/s12064-024-00414-7. Online ahead of print.ABSTRACTWe consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of...
Source: Theory in Biosciences - March 9, 2024 Category: Biology Authors: Elham Shamsara Marius E Yamakou Fatihcan M Atay J ürgen Jost Source Type: research
Dynamics of neural fields with exponential temporal kernel
Theory Biosci. 2024 Mar 9. doi: 10.1007/s12064-024-00414-7. Online ahead of print.ABSTRACTWe consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of...
Source: Theory in Biosciences - March 9, 2024 Category: Biology Authors: Elham Shamsara Marius E Yamakou Fatihcan M Atay J ürgen Jost Source Type: research
Dynamics of neural fields with exponential temporal kernel
Theory Biosci. 2024 Mar 9. doi: 10.1007/s12064-024-00414-7. Online ahead of print.ABSTRACTWe consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of...
Source: Theory in Biosciences - March 9, 2024 Category: Biology Authors: Elham Shamsara Marius E Yamakou Fatihcan M Atay J ürgen Jost Source Type: research
Behavioral selection in structured populations
Theory Biosci. 2024 Mar 5. doi: 10.1007/s12064-024-00413-8. Online ahead of print.ABSTRACTThe multilevel model of behavioral selection (MLBS) by Borgstede and Eggert (Behav Process 186:104370. 10.1016/j.beproc.2021.104370 , 2021) provides a formal framework that integrates reinforcement learning with natural selection using an extended Price equation. However, the MLBS is so far only formulated for homogeneous populations, thereby excluding all sources of variation between individuals. This limitation is of primary theoretical concern because any application of the MLBS to real data requires to account for variation betwee...
Source: Theory in Biosciences - March 5, 2024 Category: Biology Authors: Matthias Borgstede Source Type: research
Behavioral selection in structured populations
Theory Biosci. 2024 Mar 5. doi: 10.1007/s12064-024-00413-8. Online ahead of print.ABSTRACTThe multilevel model of behavioral selection (MLBS) by Borgstede and Eggert (Behav Process 186:104370. 10.1016/j.beproc.2021.104370 , 2021) provides a formal framework that integrates reinforcement learning with natural selection using an extended Price equation. However, the MLBS is so far only formulated for homogeneous populations, thereby excluding all sources of variation between individuals. This limitation is of primary theoretical concern because any application of the MLBS to real data requires to account for variation betwee...
Source: Theory in Biosciences - March 5, 2024 Category: Biology Authors: Matthias Borgstede Source Type: research
Behavioral selection in structured populations
Theory Biosci. 2024 Mar 5. doi: 10.1007/s12064-024-00413-8. Online ahead of print.ABSTRACTThe multilevel model of behavioral selection (MLBS) by Borgstede and Eggert (Behav Process 186:104370. 10.1016/j.beproc.2021.104370 , 2021) provides a formal framework that integrates reinforcement learning with natural selection using an extended Price equation. However, the MLBS is so far only formulated for homogeneous populations, thereby excluding all sources of variation between individuals. This limitation is of primary theoretical concern because any application of the MLBS to real data requires to account for variation betwee...
Source: Theory in Biosciences - March 5, 2024 Category: Biology Authors: Matthias Borgstede Source Type: research
Behavioral selection in structured populations
Theory Biosci. 2024 Mar 5. doi: 10.1007/s12064-024-00413-8. Online ahead of print.ABSTRACTThe multilevel model of behavioral selection (MLBS) by Borgstede and Eggert (Behav Process 186:104370. 10.1016/j.beproc.2021.104370 , 2021) provides a formal framework that integrates reinforcement learning with natural selection using an extended Price equation. However, the MLBS is so far only formulated for homogeneous populations, thereby excluding all sources of variation between individuals. This limitation is of primary theoretical concern because any application of the MLBS to real data requires to account for variation betwee...
Source: Theory in Biosciences - March 5, 2024 Category: Biology Authors: Matthias Borgstede Source Type: research
Optimal dispersal and diffusion-enhanced robustness in two-patch metapopulations: origin's saddle-source nature matters
Theory Biosci. 2024 Feb;143(1):79-95. doi: 10.1007/s12064-023-00411-2. Epub 2024 Feb 21.ABSTRACTA two-patch logistic metapopulation model is investigated both analytically and numerically focusing on the impact of dispersal on population dynamics. First, the dependence of the global dynamics on the stability type of the full extinction equilibrium point is tackled. Then, the behaviour of the total population with respect to the dispersal is studied analytically. Our findings demonstrate that diffusion plays a crucial role in the preservation of both subpopulations and the full metapopulation under the presence of stochasti...
Source: Theory in Biosciences - February 21, 2024 Category: Biology Authors: Marc Jorba-Cusc ó Ruth I Oliva-Z úniga Josep Sardany és Daniel P érez-Palau Source Type: research
Optimal dispersal and diffusion-enhanced robustness in two-patch metapopulations: origin's saddle-source nature matters
Theory Biosci. 2024 Feb;143(1):79-95. doi: 10.1007/s12064-023-00411-2. Epub 2024 Feb 21.ABSTRACTA two-patch logistic metapopulation model is investigated both analytically and numerically focusing on the impact of dispersal on population dynamics. First, the dependence of the global dynamics on the stability type of the full extinction equilibrium point is tackled. Then, the behaviour of the total population with respect to the dispersal is studied analytically. Our findings demonstrate that diffusion plays a crucial role in the preservation of both subpopulations and the full metapopulation under the presence of stochasti...
Source: Theory in Biosciences - February 21, 2024 Category: Biology Authors: Marc Jorba-Cusc ó Ruth I Oliva-Z úniga Josep Sardany és Daniel P érez-Palau Source Type: research
Optimal dispersal and diffusion-enhanced robustness in two-patch metapopulations: origin's saddle-source nature matters
Theory Biosci. 2024 Feb;143(1):79-95. doi: 10.1007/s12064-023-00411-2. Epub 2024 Feb 21.ABSTRACTA two-patch logistic metapopulation model is investigated both analytically and numerically focusing on the impact of dispersal on population dynamics. First, the dependence of the global dynamics on the stability type of the full extinction equilibrium point is tackled. Then, the behaviour of the total population with respect to the dispersal is studied analytically. Our findings demonstrate that diffusion plays a crucial role in the preservation of both subpopulations and the full metapopulation under the presence of stochasti...
Source: Theory in Biosciences - February 21, 2024 Category: Biology Authors: Marc Jorba-Cusc ó Ruth I Oliva-Z úniga Josep Sardany és Daniel P érez-Palau Source Type: research
Optimal dispersal and diffusion-enhanced robustness in two-patch metapopulations: origin's saddle-source nature matters
Theory Biosci. 2024 Feb;143(1):79-95. doi: 10.1007/s12064-023-00411-2. Epub 2024 Feb 21.ABSTRACTA two-patch logistic metapopulation model is investigated both analytically and numerically focusing on the impact of dispersal on population dynamics. First, the dependence of the global dynamics on the stability type of the full extinction equilibrium point is tackled. Then, the behaviour of the total population with respect to the dispersal is studied analytically. Our findings demonstrate that diffusion plays a crucial role in the preservation of both subpopulations and the full metapopulation under the presence of stochasti...
Source: Theory in Biosciences - February 21, 2024 Category: Biology Authors: Marc Jorba-Cusc ó Ruth I Oliva-Z úniga Josep Sardany és Daniel P érez-Palau Source Type: research
